The Fifteenth Marcel Grossmann Meeting

The following sections are included:

• Publications in this Series
• Sponsors and Acknowledgements
• Organizing Committees
• Marcel Grossmann Awards
• Preface
• Contents

This essay celebrates the 100th anniversary of the birth of Martin Ryle and the 50th anniversary of the discovery of pulsars by Jocelyn Bell and Antony Hewish. Ryle and Hewish received the 1974 Nobel Prize in Physics, the first in the area of astrophysics. Their interests strongly overlapped, one of the key papers on the practical implementation of the technique of aperture synthesis being co-authored by Ryle and Hewish. The discovery of pulsars and the roles played by Hewish and Bell are described. These key advances were at the heart of the dramatic rise of high energy astrophysics in the 1960s and led to the realisation that general relativity is central to the understanding of high energy astrophysical phenomena.

We comment on the advance in measurements of the anisotropy of the CMB spanning from when Remo Ruffini was starting his academic career and watching the field’s development to the present.

We give a brief review of the definition of the Wang-Yau quasilocal mass and discuss the evaluation of which on surfaces of unit size at null infinity of an axi-symmetric spacetime in Bondi-van der Burg-Metzner coordinates.

We start by looking at why we believe that black holes have entropy. According to Boltzmann, the entropy is a measure of the number of microstates of a system. We suggest here that the entropy arises from a holographic conformal field theory on the black hole horizon. Finally, we discuss some of the implications for the information paradox.

In these proceedings, I will review an obstruction for theories of the beginning of the universe which can be formulated as semiclassical path integrals. Hartle and Hawking’s no boundary proposal and Vilenkin’s tunneling proposal are examples of such theories. Each may be formulated as the quantum amplitude for obtaining a final 3-geometry by integrating over 4-geometries. The result is obtained using a new mathematical tool – Picard-Lefschetz theory – for defining the semiclassical path integral for gravity. The Lorentzian path integral for quantum cosmology with a positive cosmological constant is mathematically meaningful in this approach, but the Euclidean version is not. Framed in this way, the resulting framework and predictions are unique. Unfortunately, the outcome is that primordial gravitational wave fluctuations are unsuppressed.

In this work, we extend our previous blind GW signal estimation method to the case of multiple detectors and show that, with a full use of redundancy, it gives promising results, e.g. a faster decay of fluctuations than that expected from the central limit theorem. This method, whose design explicitly accounts for redundancy in multiple measurements, considerably improves the efficiency of signal extraction in a multi-detector network.

KAGRA is an interferometric gravitational-wave detector with 3-km arms constructed at Kamioka, Gifu, Japan. One of the key features of KAGRA is the cryogenic mirrors for the 3 km arm cavities. KAGRA plans to begin the operation before the end of 2019. KAGRA plans to join the network observation of global gravitational wave interferometers.

In this talk, I give a brief introduction to the TianQin project, which aims to start space-based gravitational wave detection in the 2030s. My main focus will be on the background, the preliminary concept, the scientific objectives, the development of key technologies, the current progress and the international collaboration of the project.

Analytic approximation methods in general relativity play a very important role when analyzing the gravitational wave signals recently discovered by the LIGO & Virgo detectors. In this contribution, we present the state-of-the-art and some recent developments in the famous post-Newtonian (PN) or slow-motion approximation, which has successfully computed the equations of motion and the early inspiral phase of compact binary systems. We discuss also some interesting interfaces between the PN and the gravitational self-force (GSF) approach based on black-hole perturbation theory, and between PN and the post-Minkowskian (PM) approximation, namely a non-linearity expansion valid for weak field and possibly fast-moving sources.

Dark Matter Particle Explorer (DAMPE), the first Chinese astronomical satellite, was launched into a Sun-synchronous orbit at an altitude of about 500 km on 17 December 2015. DAMPE is a high-energy particle detector optimized for observations of cosmic ray electrons and gamma-rays up to about 10 TeV. The on-orbit performance of the detector, the calibration, and the latest results on cosmic rays and gamma-rays of DAMPE will be presented.

Binary driven hypernova (BdHN) models long gamma-ray burst (GRBs) as occurring in the binary systems involving a carbon-oxygen core (CO_core) and a companion neutron star (NS) or a black hole (BH). This model, first proposed in 2012, succeeds and improves upon the fireshell model and the induced gravitational collapse (IGC) paradigm. After nearly a decade of development, the BdHN model has reached a nearly complete structure, giving explanation to all the observables of long bursts into its theoretical framework, and has given a refined classification of long GRBs according to the original properties of the progenitors. In this article, we present a summary of the BdHN model and the physical processes at work in each of the envisaged Episodes during its occurrence and lifetime, duly contextualized in the framework of GRB observations.

After updating the status of the measurements of the cosmic neutrino flux by the IceCube experiment, we summarize the observations of the first identified source of cosmic rays and speculate on the connection between the two observations.

We review our recent theoretical results about inequivalence between passive and active gravitational masses and energy in the semiclassical variant of general relativity, where the gravitational field is not quantized but matter is quantized. To this end, we consider the simplest quantum body with internal degrees of freedom — a hydrogen atom. We concentrate our attention on the following physical effects, related to electron mass. The first one is the inequivalence between passive gravitational mass and energy at the microscopic level. Indeed, the quantum measurement of gravitational mass can give a result which is different from the expected one, $m\ne m_e+\frac{E_1}{c^2}$, where the electron is initially in its ground state; m_e is the bare electron mass. The second effect is that the expectation values of both the passive and active gravitational masses of stationary quantum states are equivalent to the expectation value of the energy. The most spectacular effects are the inequivalence of the passive and active gravitational masses and the energy at the macroscopic level for an ensemble of coherent superpositions of stationary quantum states. We show that, for such superpositions, the expectation values of passive and active gravitational masses are not related to the expectation value of energy by Einstein’s famous equation, $m\ne \frac{E}{c^2}$. In this paper, we also improve several drawbacks of the original pioneering works.

Cosmological and astrophysical surveys from radio to far-infrared, in both temperature and polarization, offer a unique view of the Universe properties and of the formation and evolution of its structures. The last release, close to be finalized, of the Planck mission results sets the scene for cosmological models and parameters, while the comparison with other types of data sets raises the issue of possible tensions about some parameters, first of all the Hubble constant. At the same time, on the extragalactic side, Planck carried out the deepest systematic all-sky survey of SZ galaxy clusters and detected thousands of dusty galaxies and many hundreds of extragalactic radio sources, also allowing us to investigate many specific topics, including molecular hydrogen clouds in galactic halos. The exploitation of future generation of CMB missions and the next radio facilities will allow us to deeply investigate several topics in cosmology and astrophysics, from the existence of primordial gravitational waves to the energy releases in the primeval plasma, from the dawn ages and the epoch of reionization to the formation and evolution of early galaxies and clusters, while a wide set of open astrophysical problems can be studied with future IR missions.

Understanding accretion flow dynamics around black hole (BH) sources one needs to make detailed study of spectral as well as temporal properties of these objects during their active phases. We believe that studying accretion flow properties of BHs, it is necessary analyze observed data with a generalized physical model. Recently after the implementation of the generalized two Component Advective Flow (TCAF) solution as a local additive table model into HeaSARC’s spectral analysis package XSPEC, a more clear picture about the flow nature around the BHs are obtained. TCAF model fitted spectral parameters (two types of accretion rates: Keplerian disk and sub-Keplerian halo, and two types of shock parameters: location and strength of the shock) allow us to find a better physical picture about the physical processes associated with BHs. One can also predict frequency of primary dominating QPOs from TCAF model fitted shock parameters. Based on evolution of halo to disk accretion rate ratio (ARR), quasi-periodic oscillation (QPOs; if present) frequencies, a physical understanding of different observed spectral states and their transitions are done. We are able to estimate intrinsic source parameters (mass, spin), jet X-ray fluxes, etc. from spectral analysis with TCAF model. This makes this model as an ideal tool to study BHs.

We study the modulation of the observed radiation flux and the associated changes in the polarization degree and angle that are predicted by the orbiting spot model for flares from accreting black holes. The geometric shape of the emission region influences the resulting model lightcurves, namely, the emission region of a spiral shape can be distinguished from a simpler geometry of a small orbiting spot.

We further explore this scheme for the observed flares from the supermassive black hole in the context of Galactic center (Sgr A^*). Our code simulates the lightcurves for a wide range of parameters. The energy dependence of the changing degree and angle of polarization should allow us to discriminate between the cases of a rotating and a non-rotating black hole.

Two examples of the analysis of the hard X-ray/soft γ-ray emission from accreting black holes observed with the INTEGRAL satellite are presented. The first study is based on data covering 16 years of monitoring of the bright persistent Cyg X-1 system. This huge data set allowed us to get more insights into the geometry of the plasma region in different spectral states of the object. In particular, we identify two substates of the hard state and provide new information on the plasma behaviour during the jet emission. The second study is based on data taken during the 2015 outburst of transient black hole binary V404 Cygni. The results of detailed spectral analysis show that a single Componization component, purely thermal or hybrid, is not sufficient to explain the hard X-ray emission during a strong radio emission period.

Observational evidences show that during the outburst, black hole binaries move to different spectral states depending on accretion flow that feeds these objects. However proper physical picture is still unclear, what causes these states change and how the quasi periodic oscillation (QPO) in observed lightcurve is related with the disk properties? In a Two Component Advective Flow (TCAF) solution it is established that low angular momentum and low viscous sub-Keplerian flow produces hot corona, which up-scatters soft photons from the Keplerian disk. We analyze the outbursts data of black holes of different scales ranging from low mass to super massive observed by different satellites with TCAF and discuss the outburst features and their spectral states.

Ultra-luminous X-ray sources (ULXs) have been puzzling us with a debate whether they consist of an intermediate mass black hole or super-Eddington accretion by a stellar mass black hole. Here we suggest that in the presence of large scale strong magnetic fields and non-negligible vertical motion, the luminosity of ULXs, particularly in their hard states, can be explained with sub-Eddington accretion by stellar mass black holes. In this framework of 2.5D magnetized advective accretion flows, magnetic tension plays the role of transporting matter (equivalent to viscous shear via turbulent viscosity) and we neither require to invoke an intermediate mass black hole nor super-Eddington accretion. Our model explains the sources, like, NGC 1365 X1/X2, M82 X42.3+59, M99 X1 etc. which are in their hard power-law dominated states.

We study the bound orbit conditions for equatorial and eccentric orbits around a Kerr black hole both in the parameter space (E, L, a) representing the energy, angular momentum of the test particle, and spin of the black hole, and also (e, μ, a) space representing the eccentricity, inverse-latus rectum of the orbit, and spin. We apply these conditions and implement the relativistic precession (RP) model to M82X-1, which is an Intermediate-mass black hole (IMBH) system, where two high-frequency Quasi-Periodic Oscillations (HFQPOs) and a low-frequency QPO were simultaneously observed. Assuming that the QPO frequencies can also be generated by equatorial and eccentric trajectories, we calculate the probability distributions to infer e, a, and periastron distance, r_p, of the orbit giving rise to simultaneous QPOs. We find that an eccentric orbit solution is possible in the region between innermost stable circular orbit (ISCO) and the marginally bound circular orbit (MBCO) for $e={0.2768}_{-0.0451}^{+0.0657},$ a = 0.2897 ± 0.0087, and $r_p={4.6164}_{-0.1259}^{+0.0694}$.

Accretion disks around stellar-mass black holes (BHs) are observed to emit radiation peaking in the soft X-rays (at about 1 keV) when the source is in the thermal state. This emission is expected to be polarized, because of electron scattering in the disk. However, photons will experience a rotation of the polarization plane due to General Relativity effects. X-ray polarization measurements can then be crucial in assessing strong gravity effects around accreting stellar-mass BHs, providing independent constraints on their spin. In this work, we present the simulated polarization spectra (obtained according to the model by Dovčiak et al.) for the X-ray, thermal radiation emitted by the accretion disk, as expected to be measured by IXPE, an X-ray polarimeter which will be launched in 2021. We also illustrate the code, currently under development, incorporate the contribution of returning radiation and account for absorption effects by the disk material.

The Rossby-Wave Instability (RWI) has been proposed to be at the origin of the highfrequency QPOs observed in black-hole systems. Here we are presenting the first full GR simulations of the instability around a Kerr black-hole which allow us to explore the impact of the spin on the instability. Those simulations, coupled with a full GR ray-tracing, allow us to directly compare our simulation with the observables we get through X-ray observations.

With NICER up and running and the ATHENA mission in preparation there is need to study in more detail what is the influence, if any, of the spin on the observed spectrum. Using the newly developed NOVAs framework which is comprised of a GR code, GRAM-RVAC, coupled with the ray-tracing GR code, gyoto, we computed a series of simulated disk spectrums for a variety of black-hole spins. Using standard models from xspec we fitted those spectrums and looked at how they performed to give us the parameters of the simulated spectrums. Here we report on our findings and how we could improve the existing models to get better insights into the physical large scale disk parameters.

Here we are presenting NOVAs, a Numerical Observatory of Violent Accreting systems, which couples a GR AMR MPI fluid dynamics code (GRAMRVAC) able to follow accretion around a Kerr Black-hole with the ray-tracing code GYOTO. Together, they allow us to test different models by running the simulation and obtaining spectral energy distributions and power-density spectrums from which we can extract the same observables as for ‘real’ observations, hence making it a Numerical Observatory.

A solution of the Boltzmann equation is obtained for a magnetized plasma with strongly degenerate electrons and nondegenerate nuclei. The components of the diffusion, thermal diffusion, and diffusion thermoeffect tensors in a nonquantizing magnetic field are calculated in the Lorentz approximation without allowance for electron-electron collisions, which is asymptotically accurate for plasma with strongly degenerate electrons. Asymptotically accurate analytical expressions for the electron diffusion, thermal diffusion, and diffusion thermoeffect tensors in the presence of a magnetic field are obtained. The expressions reveal a considerably more complicated dependence on magnetic field than analogous dependences derived in the previous publications on this subject.

Although regular orthogonal mesh is usually used in numerical relativity, isotropic mesh is preferable for complex fluid motions from the points of numerical accuracy and stability. Hexagonal close pack(HCP) mesh is thought to be an ideal for those purposes. However, HCP has not been used widely so far since it is difficult to implement HCP with data structures existing programming language such as C/C₊₊ or Python provides. In this paper, I propose novel coordinate system suitable to realize HCP with usual array data. In addition, Voronoi tessellation and mesh refinement of HCP is described briefly.

We address the role of large scale magnetic stress in the angular momentum transport, as well as the formation of different kinds of magnetic barrier in geometrically thick, optically thin, vertically averaged 1.5-dimensional advective accretion flows around black holes. The externally generated magnetic fields are captured by the accretion process from the environment, say, companion stars or interstellar medium. This field becomes dynamically dominant near the event horizon of a black hole due to continuous advection of the magnetic flux. In such magnetically dominated accretion flows, the accreting matter either decelerates or faces magnetic barrier in vicinity of the black hole depending on the magnetic field geometry. We find that the accumulated strong poloidal fields along with certain toroidal field geometry help in the formation of magnetic barrier which may knock the matter to infinity. When matter is trying to go back to infinity after getting knocked out by the barrier, in some cases it is prevented being escaped due to cumulative action of strong magnetic tension and gravity, and hence another magnetic barrier. We suggest, this kind of flow may be responsible for the formation of episodic jets in which magnetic field can lock the matter in between these two barriers. We also find that for the toroidally dominated disc, the accreting matter rotates very fast and decelerates towards the central black hole.

We represent results of simulation protostellar molecular clouds(MC) collision process. The interaction of the MC with each other leads to the emergence of extremely dense, gravitationally bounded regions, which can be sources of the formation of new stars and star systems. Computer modeling was carried out on high-resolution grids up to 2048 × 1024 × 1024. Oscillations of the MC surface, which are caused by the formation of a dense lenticular structure at the interface of the colliding clouds in the process of collision, are found.

We model the propagation of pulsars through the inhomogeneous ISM using nonrelativistic axisymmetric magneto-hydrodynamic (MHD) simulations. We take into account the wind from the star, which carries predominantly azimuthal magnetic field, and investigate the PWN at different levels of magnetization (the ratio of magnetic to matter energy-densities) in the wind. We consider the interaction of PWN with large-scale and small-scale imhomogeneities in the ISM at different values of magnetization. We conclude that the inhomogeneities in the ISM can change the shapes of the bow shocks and magnetotails at different values of the magnetization.

We present the results of MHD simulation of the laboratory experiment for creating plasma jets. In the experiment on a NEODIM laser installation the plasma jet is formed as a result of the action of a powerful laser on the target. We simulated plasma flow, we chose a numerical method, boundary and initial conditions. We investigated the picture of the flow and compared it with the experiment.

We study a thin warped accretion disk around a spinning black hole in the viscous regime (i.e., α > H/R; α is the Shakura-Sunyaev viscosity parameter, H is the disk thickness and R is the radial distance), and calculate the steady state radial profile of the disk tilt angle for a wide range of relevant parameters of the system (like the Kerr parameter of the black hole). Although the inner part of such a disk was proposed to become aligned with the spin direction of the black hole by the Bardeen-Petterson effect, we show that for a reasonable range of the parameters of the system, the inner disk can stay significantly tilted with respect to the black hole spin. A tilt in the inner accretion disk can affect the observed X-ray spectral and timing features, and hence it makes the inner accretion disk particularly useful for probing the strong gravity region.

We discuss the effects of electric charging on the equilibrium configurations of magnetized, rotating fluid tori around black holes of different mass. In the context of gaseous/dusty tori in galactic nuclei, the central black hole dominates the gravitational field and it remains electrically neutral, while the surrounding material acquires some electric charge that can separate in space and exhibit non-negligible self-gravitational effects. The structure of the torus is thus influenced by the balance between the gravitational and electromagnetic forces. A cusp can develop near the inner rim even in Newtonian tori due to the charge distribution. Furthermore, it is interesting to note that stable polar clouds can emerge near the rotation axis in reminiscence of “lamp-post” scenario. For the latter, an appropriate distribution of the angular momentum and electric charge are essential.

We discuss numerical method based on Implicit completely conservative Lagrangian operator-difference scheme on triangular grid of variable structure. The method was successfully applied for the simulations of magnetorotational supernova explosion.

Theoretical and observational inferences reveal that accretion and outflows/jets are strongly correlated through fundamental conservation laws. All well-known jetted sources with accreting black hole systems indicate a signature of hot advective accretion flow and a dynamically important magnetic fields at the jet footprint. We inter-connect here the disc and outflow/jet for magnetized, viscous, optically thin, geometrically thick, 2.5-dimensional hot advective flows around black holes. The magnetic fields are captured from the environment, say interstellar medium or companion star, and dragged inward with continuous accretion process. This disc becomes magnetically dominated in vicinity of a black hole due to flux freezing. The accretion geometry as well as energetics of the accretion induced outflows/jets strongly depend on the mass and spin of the black hole, accretion rate, and magnetic field strength. We suggest, this magnetically dominated accretion powered system can easily explain the energetics of the ultraluminous X-ray sources in their hard power-law dominated states.

Ringed accretion disks (RADs) are aggregates of corotating and counterrotating toroidal accretion disks orbiting a central Kerr super-massive Black Hole (SMBH) in AGNs. The dimensionless spin of the central BH and the fluids relative rotation are proved to strongly affect the RAD dynamics. There is evidence of a strict correlation between SMBH spin, fluid rotation and magnetic fields in RADs formation and evolution. Recently, the model was extended to consider RADs constituted by several magnetized accretion tori and the effects of a toroidal magnetic field in RAD dynamics have been investigated. The analysis poses constraints on tori formation and emergence of RADs instabilities in the phases of accretion onto the central attractor and tori collision emergence. Magnetic fields and fluids rotation are proved to be strongly constrained and influence tori formation and evolution in RADs, in dependence on the toroidal magnetic fields parameters. Eventually, the RAD frame investigation constraints specific classes of tori that could be observed around some specific SMBHs identified by their dimensionless spin

In this work we consider the effects of vertical self-gravity on a magnetized neutrino-dominated accretion disk, which is supposed to be a candidate for central engine of gamma-ray bursts (GRBs). We study some of the physical timescales that are considered to play a crucial role in the disk’s late-time activity, such as viscous, cooling, and diffusion timescales. We are also interested to probe the emission of X-ray flares’ probability, observed in GRBs’ extended emission by an investigation on the “magnetic barrier” and “fragmentation”. Our results approve the self-gravity as an amplifier for Blandford–Payne luminosity (BP power) and the magnetic field produced through the accretion process, but a suppressor for neutrino luminosity and magnetic barrier. The latter takes place as a result of the fragmentation enhancement in the outer disk, which is more likely to happen for the higher mass accretion rates.

A unification of dark matter and dark energy based on a dynamical space time theory is discussed. By introducing a dynamical space time vector field χ_μ as a Lagrange multiplier, a conservation of an energy momentum tensor $\underset{\left(\chi \right)}{T^{\mu \nu }}$ is implemented in addition to the conservation of the metric energy momentum tensor. This Lagrangian generalizes the Unified dark energy and dark matter from a scalar field different from quintessence which did not consider a Lagrangian formulation. This generalization allows the solutions which were found previously, in addition to a-non singular bouncing solutions that rapidly approach to the ΛCDM model. The dynamical time vector field exactly coincides with the cosmic time for the a ΛCDM solution and suffers a slight shift (advances slower) with respect to the cosmic time in the region close to the bounce for the bouncing non singular solutions. For some exponential potential which gives a possible interaction between DE and DM and could explain the coincidence problem.

It is known that one can formulate an action in teleparallel gravity which is equivalent to general relativity, up to a boundary term. In this geometry we have vanishing curvature, and non-vanishing torsion. The action is constructed by three different contractions of torsion with specific coefficients. By allowing these coefficients to be arbitrary we get the theory which is called “new general relativity”. In this note, the Lagrangian for new general relativity is written down in ADM-variables. In order to write down the Hamiltonian we need to invert the velocities to canonical variables. However, the inversion depends on the specific combination of constraints satisfied by the theory (which depends on the coefficients in the Lagrangian). It is found that one can combine these constraints in 9 different ways to obtain non-trivial theories, each with a different inversion formula.

In this short paper we study how black hole singularities can be tackled in the context of nonlocal ghost-free gravity, in which the action is characterized by the presence of non-polynomial differential operators containing infinite order covariant derivatives. The ghost-freeness condition can be preserved by requiring that such nonlocal operators are made up of exponential of entire functions, thus avoiding the emergence of extra unhealthy poles in the graviton propagator. We will mainly focus on how infinite order derivatives can regularize the singularity at the origin by making explicit computations in the linear regime. In particular, we will show that this kind of non-polynomial operators can smear out point-like distribution and that the Schwarzschild metric can not be a solution of the field equations in the ghost-free infinite derivative gravity.

The Horizon Quantum Mechanics allows one to analyse the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. We first review the global formalism and show that it reproduces a gravitationally inspired GUP relation but also leads to unacceptably large fluctuations in the horizon size of astrophysical black holes if one insists in describing them as (smeared) central singularities. On the other hand, if they are extended systems, like in the corpuscular models, no such issue arises and one can in fact extend the formalism to include asymptotic mass and angular momentum with the harmonic model of rotating corpuscular black holes. The Horizon Quantum Mechanics then shows that, in simple configurations, the appearance of the inner horizon is suppressed and extremal (macroscopic) geometries seem highly disfavoured.

The curve in space occupied by the mass during time evolution, is a geodesic on the space-time manifold curved by the presence of masses: the mass can only follow its trajectory consistently with the underlying gravitational field. Is it possible to think at the charge trajectory in a similar fashion? Is it possible to say that the charge trajectory, the curve in phase-space occupied by the charge during time evolution, is the geodesic on the extended phase-space curved by the presence of charges? If yes then it should be possible to obtain an Einstein’s equation also for electromagnetism. This is done by considering a metric on the whole extended phase-space, which is the phase-space (x, v) plus the time, t. It is proposed to add a Hilbert-Einstein term in the lagrangian when velocities are considered as dynamical variables. Here, it will be analyzed what happens if the (non perturbative) guiding center description of motion is adopted. In such case, a similar mechanism to the one proposed by Kaluza and Klein (KK) a century ago is found. The advantage of using the present description is that, now, there is no need of looking for a compactification scheme as required in the original KK mechanism. Indeed, the extra-dimension that appears in the guiding center transformation is a physical and, in principle, measurable variable being the gyro-phase, the angle obtained when the velocity space is described by a sort of cylindrical transformation of velocities coordinates. Regardless of the equations that are really similar to the one seen in the KK mechanism, the new claim is in the interpretation of the extra dimension as a coordinate coming from the velocity space. Until now, all the compactification mechanisms have been shown to give problems, like the inconsistency of the scale of masses with observations. Instead, without a compactification at the Planck scale length and giving a physical meaning to the extra-coordinate, it seems that the KK mechanism can finally be accepted as a realistic explanation of the presence of gravitation and electromagnetism treated in a unified manner in general relativity theory extended to higher dimensions.

A little known symmetry group of Brans-Dicke gravity in the presence of conformally invariant matter (including electrovacuo) is used as a solution-generating technique, starting from a known solution as a seed. This novel technique is applied to generate, as examples, new spatially homogeneous and isotropic cosmologies, a 3-parameter family of spherical time-dependent spacetimes conformal to a Campanelli-Lousto geometry, and a family of cylindrically symmetric geometries.

We apply Relativistic Newtonian Dynamics (RND), a Lagrangian-based, metric theory to a static, spherically symmetric gravitational field. Using a variational principle and conserved momenta, we construct several metrics, analytic everywhere except at r = 0, which have g₀₁ ≠ 0 yet still leads to the same trajectories as in the Schwarzschild model. These metrics passes all classical test of GR. However, this model and GR predict different velocities on the trajectories, both for massive objects and massless particles. The total time for a radial round trip of light in RND is the same as in the Schwarzschild model, but RND allows for light rays to have different speeds propagating toward and away from the massive object. One of theses metrics keeps the speed of light toward the object to be c. We present possible experiments to test whether g₀₁ = 0. RND extends to multiple non-static forces, each of which obeys an inverse square law and whose field propagates at the speed of light.

The direct detection of gravitational waves and gamma-ray counterparts has confirmed that gravitational waves propagate with the speed of light, disruling some of the scalar-tensor gravity models. A huge class of Horndeski theories (those with generic G2 and G3, and with G4 depending only of the scalar field) however survived the test. The study of perturbations of such models is important to establish the ghost-free and instability-free parameter regimes. This has been investigated for a wide range of scalar-tensor theories in the spherically symmetric setup, exploring a 2+1+1 decomposition of space-time based on an orthogonal double foliation. The orthogonality however consumed one gauge degree of freedom, allowing the discussion of only the odd sector of the scalar part of perturbations. In order to describe the even sector perturbations, we worked out a novel 2+1+1 decomposition of space-time and gravitational dynamics, based on a non-orthogonal double foliation. We explore this new formalism for the perturbations of both the spherically symmetric metric tensor and scalar field in generic scalar-tensor theories, achieving an unambiguous gauge-fixing. This opens up the way for the discussion of the full spectrum of perturbations of spherically symmetric scalar-tensor gravity, including both the odd and even sectors of the scalar part of perturbations.

Propagating shock-waves can be discussed in terms of junction conditions between space-time regions separated by a hypersurface. Recent observations of gravitational waves and their electromagnetic counterparts established that the former also propagate with the speed of light. Hence energetic gravitational waves could be perceived as shock-waves on null hypersurfaces. The most generic scalar-tensor theories with at most second order dynamics, the Horndeski-theories were severely constrained. We derive junction conditions across a null hypersurface for the subclass of allowed Horndeski-theories with linear kinetic term dependence, exploring a formalism based on a transverse null vector. We obtain a 2+1 decomposed generalised Lanczos equation, with the jump of the transverse curvature induced by both the distributional energy-momentum tensor of the wavefront of the shock-wave, and by the jump in the transverse derivative of the scalar. The surface density, current and pressure of the distributional light-like shock-wave and the transverse derivative of the scalar are also constrained by a scalar junction equation.

f (T) gravity is a generalization of the teleparallel equivalent of general relativity (TEGR), where T is the torsion scalar made up of the Weitzenböck connection. This connection describes a spacetime with zero curvature but with nonvanishing torsion, which fully encodes the gravitational phenomena. We will present recent results in f (T) gravity related with the issue of the degrees of freedom of the theory. In particular, we discuss the recent finding that f (T) gravity has one extra degree of freedom compared with TEGR, which was concluded through a detailed Hamiltonian analysis of the constraint structure of the theory. The physical interpretation of this result at the level of the trace of the equations of motion and its comparison with the f (R) case is discussed.

In 2010, Banados and Ferreira (BF) constructed a variant of Born-Infeld (BI) gravity with a simple matter coupling and demonstrated how the standard background FRW cosmology could become free of curvature singularities (big-bang). Further investigations revealed many interesting consequences of this BF version of BI gravity. For a toy 3D version, we show a simple analytical solution exhibiting the removal of the big-bang singularity. Thereafter, we look at BI gravity coupled to scalar BI matter, where we are able to find non-singular (loitering and bounce types) background solutions with late as well as early time acceleration. Finally, we elevate the BI gravity parameter to a spacetime dependent field (in a novel Brans-Dicke like way) and demonstrate how cosmologies without singularities and with late as well as early-time acceleration can indeed arise quite naturally.

We present a novel theory of gravity, namely, an extension of symmetric teleparallel gravity. This is done by introducing a new class of theories where the nonmetricity Q is coupled nonminimally to the matter Lagrangian. This nonminimal coupling entails the nonconservation of the energy-momentum tensor, and consequently the appearance of an extra force. We also present several cosmological applications.

In this talk we discuss some classical aspects of general polynomial higher-derivative gravity. In particular, we describe the behaviour of the weak-field solutions associated to a point-like mass at small distances and provide necessary and sufficient conditions for the metric to be regular. We also consider the metric for a collapsing thick null shell, and verify that it is regular if the aforementioned conditions are valid.

We construct a two-dimensional action that is an extension of spherically symmetric Lovelock gravity. In spite that the action contains arbitrary functions of the areal radius and the norm squared of its gradient, the field equations are second order and obey the Birkhoff’s theorem. Similar to the spherically symmetric Lovelock gravity, the field equations admit the generalized Misner-Sharp mass that determines the form of the vacuum solution. The arbitrary functions in the action allow for vacuum solutions that describe a larger class of nonsingular black-hole spacetimes than previously available.

We analyze the propagation of gravitational waves in a molecular matter medium: our findings demonstrate that dispersion only is expected, together with the emergence of three extra polarizations, able to induce longitudinal stresses. We also give quantitative estimates of the predicted effects.

Construction of a model of Quantum Gravity, which will be some day in concordance with experiments, is one of the most fascinating tasks we have in modern theoretical physics. There are a plethora of common problems, which must be solved to find a viable candidate for Quantum Gravity. We introduce the concept of the nonlinear graviton and we end with possible experimental evidence for our approach.

The equation of state of an ultrarelativistic perfect fluid is obtained as a necessary condition for a perfect fluid space-time in Rastall’s cosmology.

Unimodular quantum cosmology admits wavepacket solutions that evolve according to a kind of Schrödinger equation. Though this theory is equivalent to general relativity on the classical level, its canonical structure is different and the problem of time does not occur. We present an Ehrenfest theorem for the long term evolution of the expectation value of the scale factor for a spatially flat Friedmann universe with a scalar field. We find that the classical and the quantum behavior in the asymptotic future coincide for the special case of a massless scalar field. We examine the general behavior of uncertainties in order to single out models that can lead to a classical universe.

Static coordinates can be convenient to solve the vacuum Einstein’s equations in presence of spherical symmetry, but for cosmological applications comoving coordinates are more suitable to describe an expanding Universe, especially in the framework of cosmological perturbation theory (CPT). Using CPT we develop a general method to transform in the weak field limit any static spherically symmetric (SSS) metric from static coordinates to the Newton gauge. We apply the method to the Schwarzschild de Sitter (SDS) metric to a SSS solution of the Brans-Dicke theory, confirming the results obtained independently by solving the perturbation equations in the Newton gauge. We then consider different classes of SSS metrics obtained by modifying the SDS metric and compute the corresponding Bardeen potentials. Using the gauge invariance of the Bardeen potentials we obtain a gauge invariant definition of the turn around radius, checking it is consistent with the result obtained in static coordinates for the SDS metric and for other SSS metrics.

Motivated by the symmetric teleparallel equivalent of general relativity we present a class of extended gravity theories where a scalar field is nonminimally coupled to nonmetricity Q. The Lagrange multipliers ensure that the connection is torsion free and flat. As a consequence, there exists a coordinate system where the connection coefficients vanish globally. We give the field equations for the metric, connection, and scalar field, and then briefly discuss cosmology, conformal invariance, and the relation with f(Q) theory.

This study highlights the dynamics of anisotropic universe in modified gravity. To meet this aim, locally rotationally symmetric Bianchi type I spacetime is studied in the metric theory of f(R) gravity. Anisotropic fluid is considered to study the exact solutions of modified field equations. In particular, a general solution metric is reported using the well-known power law f(R) gravity model. The graphical analysis of equation of state parameter is given which includes the corresponding values predicted for cosmic expansion. The energy conditions are also discussed for a range of specific model parameter. It is shown that anisotropic universe in modified gravity anticipate some interesting solutions and viable power law f(R) gravity models can be reconstructed using suitable values of model parameter.

We investigate the existence and stability of the Einstein universe in the context of f (R, T, Q) gravity, where Q = R_μν T^μν. Considering linear homogeneous perturbations around scale factor and energy density, we formulate static as well as perturbed field equations. We parameterize the stability regions corresponding to conserved as well as non-conserved energy-momentum tensor using linear equation of state parameter for particular models of this gravity. The graphical analysis concludes that for a suitable choice of parameters, the stable regions of the Einstein universe are obtained which indicate that the big-bang singularity can be avoided successfully by the emergent mechanism in non-minimal matter-curvature coupled gravity.

We discuss anisotropic source describing the phenomena of collapse and expansion in the context of f (R, T) theory. For this purpose, we take an auxiliary solution of the Einstein field equations and evaluate expansion scalar whose negative values lead to collapse and positive values give expansion. For both cases, the behavior of density, pressures as well as anisotropic parameter is explored and the effects of model parameter on these quantities are examined. We also check the energy conditions for physical viability of these generating solutions.

In this work we reformulate classical and quantum cosmology in terms of a tomographic description. This approach enables us to describe the quantum and classical states of the universe in the same way and allows us to examine some aspects of the transition from the initial quantum stage to the next classical one, which are not evident in the other formulations of quantum cosmology. For reasons of simplicity and because they allow us to very effectively illustrate some aspects of the quantum-classical transition, we have considered the Hartle-Hawking model for a de Sitter universe and the corresponding classical model. The analysis obtained can also be extended to the tunneling from nothing of Vilenkin-LInde, provided that some restrictions are made in the models. We demonstrate that the Hartle-Hawking model does not have a classic limit.

In our contribution we present spherically symmetric solutions in four dimensions to the Einstein-Weyl (and also general quadratic) gravity admitting arbitrary value of the cosmological constant. The main attention is paid to the black hole spacetimes representing one parameter extension of the well-known Schwarzschild-(anti-)de Sitter geometry of Einstein’s general relativity. This additional parameter corresponds to the non-vanishing value of the Bach tensor at the black hole horizon. Our work thus generalises recent paper by Lü et al. (Phys. Rev. Lett. 114 (2015) 171) to any value of the cosmological constant. Moreover, using more convenient metric ansatz, the field equations form an autonomous system and their solution is explicitly obtained in an exact form of power series. The physical interpretation of these geometries is also discussed, namely we investigate specific tidal effects on free test particles or their basic thermodynamic properties.

The f (R, T ) gravity theory was proposed as an extension of the f(R) theories, for which besides geometrical correction terms, proportional to the Ricci scalar R, one has also material correction terms, proportional to the trace of the energy-momentum tensor T. Those material extra terms prevent the energy-momentum tensor of the theory to be conserved. On the other hand, in the context of noncommutative quantum mechanics, the presence of compact dimensions whose coordinates do not commute with time imply that time evolution is discretized, a feature which induces violations of energy conservation. In the present work we propose a connection between these two effects, so that the energy nonconservation observed in the 4-dimensional f(R, T ) gravity can be understood as a macroscopic effect of nonconservative quantum transitions involving the compact extra dimension. It turns out that the energy flows between the ordinary (commutative) 4-dimensional spacetime and the compact extra dimension.

We present the effect of the quantum corrections on the Szekeres spacetime, a system important for the study of the inhomogeneities of the pre-inflationary era of the universe. The study is performed in the context of canonical quantisation in the presence of symmetries. We construct an effective classical Lagrangian and impose the quantum version of its classical integrals of motion on the wave function. The interpretational scheme of the quantum solution is that of Bohmian mechanics, in which one can avoid the unitarity problem of quantum cosmology. We discuss our results in this context.

We investigate the problem of the orbital stability of the motion of a test body in the restricted three-body problem, where all bodies have their own rotation. The stability of the orbits is investigated by using vector elements of orbits such as orbital moment and its time derivative. We show that it is possible to get some insight into the stability properties of the motion of test bodies.

We address the question of point particle motion coupled to classical fields, in the context of scalar fields derived from higher-order Lagrangians and BLTP electrodynamics.

Einstein, Infeld, and Hoffmann (EIH) claimed that the field equations of general relativity theory alone imply the equations of motion of neutral matter particles, viewed as point singularities in space-like slices of spacetime; they also claimed that they had generalized their results to charged point singularities. While their analysis falls apart upon closer scrutiny, the key idea merits our attention. This rapport identifies necessary conditions for a well-defined general-relativistic joint initial value problem of N classical point charges and their electromagnetic and gravitational fields. Among them, in particular, is the requirement that the electromagnetic vacuum law guarantees a finite field energy-momentum of a point charge. This disqualifies the Maxwell(–Lorentz) law used by EIH. On the positive side, if the electromagnetic vacuum law of Bopp, Landé– Thomas, and Podolsky (BLTP) is used, and the singularities equipped with a non-zero bare rest mass, then a joint initial value problem can be formulated in the spirit of the EIH proposal, and shown to be locally well-posed — in the special-relativistic zero-G limit. With gravitational coupling (i.e. G > 0), though, changing Maxwell’s into the BLTP law and assigning a bare rest mass to the singularities is by itself not sufficient to obtain even a merely well-defined joint initial value problem: the gravitational coupling also needs to be changed, conceivably in the manner of Jordan and Brans–Dicke.

We report on recent developments towards a relativistic quantum mechanical theory of motion for a fixed, finite number of electrons, photons, and their anti-particles, as well as its possible generalizations to other particles and interactions.

Most versions of classical physics imply that if the 4-volume of the entire space-time is infinite or at least extremely large, then random fluctuations in the matter will by coincidence create copies of us in remote places, so called “Boltzmann brains.” That is a problem because it leads to the wrong prediction that we should be Boltzmann brains. The question arises, how can any theory avoid making this wrong prediction? In quantum physics, it turns out that the discussion requires a formulation of quantum theory that is more precise than the orthodox interpretation. Using Bohmian mechanics for this purpose, we point out a possible solution to the problem based on the phenomenon of “freezing” of configurations.

Traversable Wormhole are amazing astrophysical objects predicted by General Relativity which are able to connect remote region of space-time. Even if their existence has not been proved yet they are object of continuous investigation. From the theoretically point of view, to exist, traversable wormholes need a special form of energy density termed “exotic”. Since this exotic source must be concentrated on the throat of the wormhole, we discuss the implications of assuming Yukawa-like profiles which could be realize such a configuration.

A lot can be learned about black holes and wormholes by re-scaling spacetime itself without changing the coordinates used to describe it. Such a conformal transformation is called a Weyl transformation. It takes spacetime from a given frame — called Einstein frame — to a conformal frame — called Jordan frame. Such a transformation reveals that horizons and wormholes might appear/disappear in the conformal frame even if they were absent/present in the original frame. It arises both from the simple prescription for defining black holes and wormholes, as well as from the more sophisticated definitions. In addition, some definitions might be transformed into one another under Weyl transformations.

Ever since their revival three decades ago, in the seminal work of Morris and Thorne, Lorentzian wormholes in General Relativity have led an uncomfortable existence because they require matter which violates the well-known energy conditions. However, in scalar-tensor and other theories of gravity, realistic wormholes can indeed exist with ‘normal matter’. We illustrate this with some known examples and also by explicitly constructing a zero Ricci scalar wormhole in a four dimensional scalar-tensor, on-brane gravity theory arising from the two-brane Randall-Sundrum model with one extra dimension. If such a wormhole could arise as the end-state of some astrophysical process, its ringdown may be studied using gravitational waves. With this aim, we obtain the scalar quasinormal modes in this class of wormholes and choose to identify them as for the ‘breathing mode’ associated with gravitational waves in scalar-tensor theories. Finally, if a breathing mode is indeed observed in LIGO-like detectors with design sensitivity, and has a maximum amplitude equal to that of the tensor mode that was observed of GW150914, then for a range of values of the wormhole parameters we will be able to discern it from a black hole. If in future observations we are able to confirm the existence of such wormholes, we would, at one go, have some indirect evidence of a modified theory of gravity as well as extra spatial dimensions.

Hawking’s singularity theorem concerns matter obeying the strong energy condition (SEC), which means that all observers experience a non-negative effective energy density (EED). The SEC ensures the timelike convergence property. However, for both classical and quantum fields, violations of the SEC can be observed even in the simplest of cases, like the Klein-Gordon field. Therefore there is a need to develop theorems with weaker restrictions, namely energy conditions averaged over an entire geodesic and weighted local averages of energy densities such as quantum energy inequalities (QEIs). We present lower bounds of the EED for both classical and quantum scalar fields allowing nonzero mass and nonminimal coupling to the scalar curvature. In the quantum case these bounds take the form of a set of state-dependent QEIs valid for the class of Hadamard states. We also discuss how these lower bounds are applied to prove Hawking-type singularity theorems asserting that, along with sufficient initial contraction, the spacetime is future timelike geodesically incomplete.

We consider Ellis wormholes immersed in rotating matter in the form of an ordinary complex boson field. The resulting wormholes may possess full reflection symmetry with respect to the two asymptotically flat spacetime regions. However, there arise also wormhole solutions where the reflection symmetry is broken. The latter always appear in pairs. We analyse the properties of these rotating wormholes and show that their geometry may feature single throats or double throats. We also discuss the ergoregions and the lightring structure of these wormholes.

This report is based on the Parallel Session AT3 “Wormholes, Energy Conditions and Time Machines” of the Fifteenth Marcel Grossmann Meeting - MG15, held at the University of Rome “La Sapienza” – Rome, in 2018.

Gravitational waves are probes of gravity in the strong-field regime that allow to understand the nature of compact objects. Several families of exotic compact objects have been conceived in order to overcome some paradoxes associated to black holes, particularly the existence of the event horizon. Some models of exotic compact objects are characterized by microscopic or even Planckian corrections at the horizon scale. In particular, the wormhole solution has a perfectly reflecting surface instead of the event horizon. Spinning horizonless compact objects may be unstable against an “ergoregion instability” when spinning sufficiently fast. We analyse the instability and its astrophysical impact for the viability of exotic compact objects.

Wormhole solutions in a generalized hybrid metric-Palatini matter theory, given by a gravitational Lagrangian density f (R, ℛ), where R is the metric Ricci scalar, and ℛ is a Palatini scalar curvature defined in terms of an independent connection, and a matter Lagrangian, are found. The solutions are worked out in the scalar-tensor representation of the theory, where the Palatini field is traded for two scalars, ϕ and ψ, and the gravitational term R is maintained. The main interest in the solutions found is that the matter field obeys the null energy conditions everywhere, including the throat and up to infinity, so that there is no need for exotic matter. The wormhole geometry with its flaring out at the throat is supported by the higher-order curvature terms, or equivalently, by the two fundamental scalar fields, which either way can be interpreted as a gravitational fluid. Thus, in this theory, in building a wormhole, it is possible to exchange the exoticity of matter by the exoticity of the gravitational sector.

We explore the possibility of ‘time travel’ through geodesics in the first order formulation of classical gravity theory. The analysis is developed around a few vacuum solutions to the field equations, constructed such that the proper time exhibits a non-monotonic flow along the geodesic. These geometries are built upon metrics whose determinant vanish over some region. The associated spacetimes are smooth and the curvature two-form fields are finite everywhere.

We study shadows cast, under some circumstances, by a certain class of rotating wormholes and explore the dependence of the shadows on the wormhole spin. We compare our results with that of a Kerr black hole. For small spin, the shapes of the shadows cast by a wormhole and a black hole are nearly identical to each other. However, with increasing values of the spin, the shape of a wormhole shadow start deviating considerably from that of a Kerr black hole. Detection of such considerable deviation in future observations may possibly indicate the presence of a wormhole. In other words, our results indicate that the wormholes which are considered in our work and have reasonable spin can be distinguished from a black hole, through the observation of their shadows.

The BRST-BV formalism provides a general and systematic framework to classify consistent deformations of gauge theories. This note is a brief review of the generalization of the method to accommodate the treatment of massive field theories in the Stueckelberg formulation. Applications include the classification of the cubic and quartic interaction vertices for a multiplet of massive spin-1 fields, and of the cubic deformations of the theory of a single massive spin-2 field. The results are shown to correctly reproduce the known vertices of massive Yang–Mills theory and massive gravity, respectively. The formalism also sheds light on the characterization of Stueckelberg gauge theories, by demonstrating in particular that they can be abelianized by means of local field redefinitions.

We consider a general Einstein–scalar–Gauss-Bonnet theory with a coupling function f (ϕ) between the scalar field and the quadratic gravitational Gauss-Bonnet term. We show that the existing no-hair theorems are easily evaded, and therefore black holes may emerge in the context of this theory. Indeed, we demonstrate that, under mild only assumptions for f (ϕ), asymptotic solutions describing either a regular black-hole horizon or an asymptotically-flat solution always emerge. We then show, through numerical integration, that the field equations allow for the smooth connection of these asymptotic solutions, and thus for the construction of a complete, regular black-hole solution with non-trivial scalar hair. We present and discuss the physical characteristics of a large number of such solutions for a plethora of coupling functions f (ϕ). Finally, we investigate whether pure scalar-Gauss-Bonnet black holes may arise in the context of our theory when the Ricci scalar may be altogether ignored.

We investigate the general approach to finding exact cosmological solutions in f (R) Hořava-Lifshitz gravity, based on Noether’s theorem. A feature of this approach is that it uses the behavior of an effective Lagrangian under infinitesimal transformations of the desired symmetry, explicitly determining the form f (R) for which such symmetries exist. It is shown that the dynamics of the scale factor changes according to either a exponential function of time.

We propose a novel class of degenerate higher-order scalar-tensor theories as an extension of mimetic gravity. By performing a noninvertible conformal transformation on “seed” scalar-tensor theories which may be nondegenerate, we can generate a large class of theories with at most three physical degrees of freedom. We identify a general seed theory for which this is possible. Cosmological perturbations in these extended mimetic theories are also studied. It is shown that either of tensor or scalar perturbations is generically plagued with ghost/gradient instabilities. See Ref. 1 for more details.

The constructive gravity programme applied to electrodynamics with vacuum birefringence yields the — up to unknown gravitational constants — unique compatible gravity theory for the underlying non-metric geometry. Starting from a perturbative variant of this procedure, we solve the resulting gravitational field equations for the geometry perturbation and point out the non-metric refinements to the linear Schwarzschild and the gravitational wave solution.

The constructive gravity program demands to derive the dynamics for the background geometry of some prescribed matter theory as the solution of a set of partial differential equations – so called gravitational closure equations – whose coefficient functions can be calculated directly from the prescribed matter action. Finding general solutions to the closure equations is hard to achieve in practice. A suitable symmetry reduction of the constructive gravity program will be demonstrated that allows to insert symmetries directly into the closure equations. Using cosmological symmetries – spatial homogeneity and isotropy – enables one to derive the Friedmann equations without Einstein equations for Maxwell electrodynamics as matter input. Studying general linear electrodynamics as a refined matter input, the way towards refined Friedmann equations is laid out.

In this manuscript, we will discuss the construction of covariant derivative operator in quantum gravity. We will find it is more perceptive to use affine connections more general than metric compatible connections in quantum gravity. We will demonstrate this using the canonical quantization procedure. This is valid irrespective of the presence and nature of sources. General affine connections can introduce new scalar fields in gravity.

In this paper, we present a brief account of a generic premetric gravity model based an the energy-momentum conservation law. Our main goal is to discuss the generic properties of the gravitational constitutive pseudotensor. We present irreducible decomposition of this object under the permutation group, or, equivalently, under the general linear group GL(4, ℝ). Even when the consideration is restricted to the metric ansatz, the nontrivial skewon and axion parts emerge. A special choice of the free dimensionless parameters recovers the standard GR in its premetric version.

The basics of the premetric approach are discussed, including the essential details of the formalism and some of its beautiful consequences. We demonstrate how the classical electrodynamics can be developed without a metric in a quite straightforward way: Maxwell’s equations, together with the general response law for material media, admit a consistent premetric formulation. Furthermore, we show that in relativistic theories of gravity, the premetric program leads to a better understanding of the interdependence between topological, affine, and metric concepts.

The notion of observers’ and their measurements is closely tied to the Lorentzian metric geometry of spacetime, which in turn has its roots in the symmetries of Maxwell’s theory of electrodynamics. Modifying either the one, the other or both ingredients to our modern understanding of physics, requires also a reformulation of the observer model used. In this presentation we will consider a generalized theory of electrodynamics, so called local and linear premetric, or area metric, electrodynamics and its corresponding spacetime structure. On this basis we will describe an observer’s measurement of time and spatial length. A general algorithm how to determine observer measurements will be outlined and explicitly applied to a first order premetric perturbation of Maxwell electrodynamics. The latter contains for example the photon sector of the minimal standard model extension. Having understood an observer’s measurement of time and length we will derive the relativistic observables time dilation and length contraction. In the future a modern relativistic description of the classical test of special relativity shall be performed, including a consistent observer model.

We present a method of constructing perturbative equations of motion for the geometric background of any given tensorial field theory. Requiring invariance of the gravitational dynamics under spacetime diffeomorphisms leads to a PDE system for the gravitational Lagrangian that can be solved by means of a power series ansatz. Furthermore, in each order we pose conditions on the causality of the gravitational equations, that ensure coevolution of the matter fields and the gravitational background is possible, i.e. gravitational equations and matter equations share the same initial data hypersurfaces.

In the young field of constructive gravity, the gravity theory constructed from general linear electrdynamics has been frequently used as a physically meaningful text case for the entire approach. Based on a Newtonian approximation of area metric gravity, we use the rotation curves of low surface brightness galaxies to determine ranges for the gravitational constants in this weak field limit. Thus we are able to show that even by using very simple models for the distribution of visible matter in the galaxies, Newtonian area metric gravity yields reasonable rotation curves and consistent estimates for the gravitational constants. Area-metric gravity turns out to not be an alternative to dark matter, but to reduce the dark matter fraction and to remove the need for a distribution subtantially different from visible matter.

Constructive gravity allows to calculate the Lagrangian for gravity, provided one previously prescribes the Lagrangian for all matter fields on a spacetime geometry of choice. We explain the physical and mathematical foundation of this result and point out how to answer questions about gravity that previously could not be meaningfully asked.

There are numerous reasons to study modifications of general relativity and the Standard Model of particle physics, ranging from modelling inflation to exploring galaxy rotation curves and the nature of dark matter. Here we study the most general linear theory of electromagnetism, which admits vacuum birefringence, and derive weak gravitational field equations for the underlying area metric spacetime geometry. We discuss the weak gravitational field sourced by a point mass in an area metric spacetime and find first order corrections to the linearized Schwarzschild metric of general relativity.

The most general theory of electrodynamics with linear field equations introduces a new geometry, the area metric, that regulates the propagation of light rays and massive particles instead of the usual Lorentzian metric. In the majority of the experimental situations, the area metric is expected to be a small perturbation around a metric background. In this perturbative case, two interesting results can be achieved. First, the dynamics of the area metric can be found explicitly. Second, the relative quantum theory of electrodynamics can be shown to be renormalizable and can be used to compute various fundamental processes.

I will show that, when one combines the results of quantum electrodynamics with the dynamics of an area-metric perturbation, the anomalous magnetic moment of the electron, the cross sections of Bhabha scattering, and the hyperfine splitting of the hydrogen pick up a dependence on the position. This way, measurements of the position dependence of these quantities provide a new channel to investigate area-metric deviations from a metric spacetime.

The gravitational closure of given matter field dynamics provides diffeomorphisminvariant dynamics for the very background geometry that is ultralocally employed in the matter action. Conceptual and technical key to this construction is the principal polynomial of the initially given matter field equations, which crucially depends on how exactly the background geometry makes its appearance in the matter action. In this talk, we consider two very different matter theories that employ a background geometry consisting of two Lorentzian metrics in vastly different ways. Applying the gravitational closure mechanism we derive the remarkable result that they share the same underlying gravitational dynamics.

The causal structure of given matter field equations provides the crucial input from which the constructive gravity program starts. It is therefore of paramount importance to successfully address a number of subtle issues, which do not arise in the simplest examples in the mathematical literature, but urgently must be taken into account for physically realistic models. This talk presents a recipe to handle these complications. In particular, we will focus on how to deal with non-scalar systems of equations, gauge symmetries and implicit information that needs to be made explicit before the causal structure, encoded in the so-called principal polynomial, can be calculated correctly.

The following sections are included:

• Definition of the theory and its canonical formulation
• Quantization: propagators and the superficial degree of divergence
• Gravitational waves and observational bounds
• Acknowledgments
• References

We identify the proper geometry underlying non-relativistic string theory as ‘String Newton-Cartan Gravity’. It has the distinguishing feature that one-dimensional foliation in Newton-Cartan geometry is replaced by a two-dimensional foliation on the target space. We discuss some basic properties of the string Newton-Cartan space-time, in particular it’s behaviour under T-duality transformations. This leads to interesting nonrelativistic conformal field theories at the boundary that have applications in condensed matter physics.

We present a systematic technique to expand the Einstein–Hilbert Lagrangian in inverse powers of the speed of light squared. The corresponding result for the non-relativistic gravity Lagrangian is given up to next-to-next-to-leading order. The techniques are universal and can be used to expand any Lagrangian theory whose fields are a function of a given parameter.

In this talk, we review the construction of two three-dimensional non-relativistic pure supergravity theories. One of these yields a supersymmetrization of Newton-Cartan gravity. The other one is a Chern-Simons theory with different bosonic equations of motion and matter couplings than Newton-Cartan gravity. We comment on the prospect of using these theories to construct non-relativistic supersymmetric field theories in curved backgrounds, that can be amenable to exact non-perturbative analysis via localization techniques.

We review how the large c expansion of General Relativity leads to an effective theory in the form of Twistless Torsional Newton-Cartan gravity. We show how this is a strong field expansion around the static sector of General Relativity and illustrate this through two examples.

We have used data sets from Type Ia supernova (SN Ia) and Baryon Acoustic Oscillations (BAO) to place constraints on a chameleon model of dark energy in which tachyon scalar field plays the role of chameleon field. In our analysis the exponential and nonexponential forms for the non-minimal coupling function and tachyonic potential have been assumed.

Density perturbations in the cosmic microwave background within general f (R, ϕ) models of gravity are presented. The general dynamical equations for the tensor and scalar modes in any f (R, ϕ) gravity model are provided. An application of the equations to the (varying power)-law modified gravity toy-model is then given. Based on the latest observations of the density perturbations in the sky, the model requires inflation to occur at an energy scale less than the GUT-scale (10¹⁴ GeV). The density perturbations obtained from observations are recovered naturally, with very high precision, and without fine tuning the model’s parameters.

We revise the cosmological concordance paradigm assuming dark matter shows nonvanishing pressure. We propose a Lagrangian for matter field with a Lagrange multiplier as constraint. In addition, we add a symmetry breaking effective potential accounting for the classical cosmological constant problem. To face out the fine-tuning issue, we investigate two phases: before and after transition due to the symmetry breaking. Investigating the conserved Noether current due to the shift symmetry, we show that our Lagrangian does not depend upon the scalar field φ before and after transition. We propose that during the transition the dark matter sector cancels out the effects due to quantum field vacuum energy. This process induces a positive increase of Helmotz’s free-energy which naturally leads to a negative pressure, which turns out to be constant since the sound speed naturally vanishes. The order of magnitude of the pressure is determined by visible matter only or by the bare cosmological constant. The numerical bounds over the pressure and matter densities are in agreement with current observations, alleviating the coincidence problem. Finally assuming a thermal equilibrium between the bath and our effective matter fluid, we estimate the mass associated to the dark matter candidate. Our bounds seem to be compatible with the most recent predictions over WIMP masses for fixed spin and temperature.

We discuss constraints to some nonminimally (NMC) coupled curvature-matter models of gravity by means of Solar System experiments.

First we discuss a NMC gravity model which constitutes a natural extension of 1/Rⁿ gravity to the nonminimally coupled case. Such a NMC gravity model is able to predict the observed accelerated expansion of the Universe. Differently from the f (R) = 1/Rⁿ gravity case, which is not compatible with Solar System observations, it turns out that this NMC model is a viable theory of gravity.

Then we consider a further NMC gravity model which admits Minkowski spacetime as a background, and we derive the 1/c expansion of the metric. The nonrelativistic limit of the model is not Newtonian, but contains a Yukawa correction. We look for trajectories around a static, spherically symmetric body. Since in NMC gravity the energy-momentum tensor of matter is not conserved, then the trajectories deviate from geodesics. We use the NMC gravity model to compute the perihelion precession of planets and we constrain the parameters of the model from radar observations of Mercury.

Our proposal is suggested by the presence of still open problems in Astrophysics and Cosmology. In fact the Standard Cosmological Model, even if in agreement with the experiments on several Phenomena, features strange structure, with the presence of the “Magic” Contribute of Dark Matter and Dark Energy that reaches 96% of the total. At a closer glance the principal open problems in Astrophysics and Cosmology are:

• In the observed Universe the matter prevails on antimatter even if both are always created together;
• CMB is not anisotropic nor inhomogeneous enough to be compatible with the Big Bang model without the introduction of a still unknown interaction driving the inflation;
• Given the gravity we expect a negative acceleration of the expansion. On the contrary that seems to accelerate;
• The gravitational field of Galaxies, clusters and even of the Solar system seems much stronger that the one due to the visible matter…

The first step to complete physical theories is to contemplate on the axiomatic character of the principles. This principle of relativity was formulated by Galileo and used by Newton to derive the laws of motion, and later was placed by Einstein at the center of the Special Theory and the General Relativity. This work considers the general principle of relativity as an expression of the inherent characteristic of the most important quantity in physics - the energy - that states that the energy is constant and is independent of the type or speed of movement of an object. The energy of an object is expressed as one entity that equals the sum of two energy expressions with different character. One of these two terms is denoted as the exposed energy with a kinetic character and represents the magnitude of the field of an object. This new definition of the energy offers several perspectives that are valid for both the classical and relativistic physics and provides insights beyond these two as: i) it leads to a coherent and complete model that relates the energy with the momentum and the force, ii) enables to construct the lagrangian that can be used to derive the equations of motion without artifices, iii) offers an original viewpoint on the dark matter and dark energy that is coherent with recent developments. Einstein was the first to deny the separate existence of gravitation and electromagnetism and has implied that the goal of a unified theory would be to explain the existence and to calculate the properties of matter. He revolutionized the use of the principles of symmetry in deriving the physical laws. It is known that the classical and quantum domain do not overlap and one would not expect the same governing symmetry principles in both domains. To calculate the properties of matter we employ spatial parameters that are related with the energy state of an object and the force that it exhibits. The mechanism assumes the common origin of different forces at the highest energy level. These spacetime parameters can be used to derive the electric and gravitational forces through a single mechanism that respects the LT dimensional analysis using neither the electrical charge nor the gravitational constant.

The parallel session AT7 of the 15th Marcel Grossmann Meeting held in Rome, Italy on July 1-7, 2018 is summarized. In particular, we briefly discuss each talk, highlighting the principal results and the most intriguing perspectives.

Stellar-mass black holes come from the deaths of massive stars, and have been observed both in our own Galaxy and in other galaxies. Supermassive black holes have masses of up to 10,000,000,000 times the mass of the Sun and reside at the centers of galaxies. Intermediate-mass black holes (IMBHs), with masses in between these two regimes, are elusive and represent the missing link. When a compact object ventures too close the IMBH, it is captured because of the emission of gravitational waves, to be eventually swallowed whole when it crosses the event horizon. The process, an intermediate-mass ratio inspiral, represents a mapping of warped spacetime and can be observed with existing gravitational-wave ground-based detectors. Depending on the dynamical parameters, IMRIs can be detected jointly with space-borne ones, which will allow us to do multi-band width gravitational-wave astronomy.

We compare two action integrals and identify the Lagrangian multiplier to set up a constraint equation on cosmological expansion. This is a direct result of the fourth equation of our manuscript which unconventionally compares the general-relativity action integral with the second derived action integral. This leads to Eq. (3)–(5), a bound on the cosmological constant. We replace the Hamber quantum-gravity reference-based action integral with a result from Klauder’s “Enhanced Quantization,” while showing its relevance to early-universe black-hole production and the volume of space producing 100 black holes of 10² Planck mass in a radius of 10³ Planck length for entropy of about 1000.

The first observational indication of the gravitomagnetic monopole is reported, based on the X-ray observations of an astrophysical collapsed object: GRO J1655-40. Earlier, the three independent primary X-ray observational methods gave significantly different spin values for GRO J1655-40. We show that the inclusion of an extra parameter, corresponding to the gravitomagnetic monopole, makes the spin and other parameter values inferred from the three methods consistent with each other. In addition, our result weakly indicates that GRO J1655-40 could also be a naked singularity.

We study the Kerr–Newman black hole in the formalism of isolated horizons using a general solution found by Krishnan in 2012. It establishes the existence of a null tetrad which is tangent to the horizon and parallelly propagated off the horizon along a non-twisting null geodesic congruence. However, the explicit construction of such a tetrad for the Kerr–Newman metric was not given. We have formulated appropriate initial data and found the exact form (up to integrals) of the solution everywhere in the Kerr– Newman space-time. In the near future we aim to apply this formulation to the study of distorted black holes by perturbing the initial data found in this work.

Astrophysical black holes are thought to be Kerr solution of general relativity but their Kerr geometry have not yet verified. Iron line is prominent feature in X-ray reflection spectra. Shape of iron line in X-ray reflection spectra of both stellar-mass and super massive black hole candidates are supposed to be strongly affected by spacetime geometry. This method is a powerful technique to prob strong gravity regime and deviations from Kerr spacetime. In this talk, I present iron line of some non-Kerr spacetimes. I also present data simulations of X-ray missions. The purpose is to understand whether X-ray reflection spectroscopy can distinguish these non-Kerr spacetimes from Kerr solution of general relativity.

Super-Massive Black Holes reside in galactic nuclei, where they exhibit episodic bright flares due to accretion events. Taking into account relativistic effects, namely, the boosting and lensing of X-ray flares, we further examine the possibility to constraint the mass of the SMBH from the predicted profiles of the observed light curves. To this end, we have studied four bright flares from Sagittarius A*, which exhibit an asymmetric shape consistent with a combination of two intrinsically separate peaks that occur with a specific time delay with respect to each other. We have thus proposed (Karssen et al. 2017, Mon. Not. R. Astron. Soc. 472, 4422) that an interplay of relativistic effects could be responsible for the shape of the observed light curves and we tested the reliability of the method.

The quintessence is one of the several candidates which represents the dark energy responsible for the acceleration of the universe. The quintessence is described by a canonical scalar field minimally coupled to gravity. We study the timelike geodesic congruences in the background of a rotating black hole spacetime surrounded by quintessence in equatorial plane. The effect of equation of state (EOS) parameter for quintessence and the normalization factor on geodesics is investigated in detail in view of the structure of possible orbits, including the innermost stable circular orbits (ISCOs). The structure of photon orbits is also studied for the different values of parameters involved in. The results obtained are also then compared with those of the Kerr black hole spacetime and Schwarzschild black hole spacetime in GR with or without quintessence.

The following sections are included:

• Introduction
• The orbit of a spinning particle
• Collisional Penrose process
• References

We derive the conditions for a non-equatorial eccentric bound orbit to exist around a Kerr black hole in two-parameter spaces: the energy, angular momentum of the test particle, spin of the black hole, and Carter’s constant space (E, L, a, Q), and eccentricity, inverselatus rectum space (e, μ, a, Q). These conditions distribute various kinds of bound orbits in different regions of the (E, L) and (e, μ) planes, depending on which pair of roots of the effective potential forms a bound orbit. We provide a prescription to select these parameters for bound orbits, which are useful inputs to study bound trajectory evolution in various astrophysical applications like simulations of gravitational wave emission from extreme-mass ratio inspirals, relativistic precession around black holes, and the study of gyroscope precession as a test of general relativity.

We present a smooth extension of the Schwarzschild exterior geometry, where the singular interior is superceded by a vacuum phase with vanishing metric determinant. Unlike the Kruskal-Szekeres continuation, this solution to the first order field equations in vacuum has no singularity in the curvature two-form fields, no horizon and no global time. The underlying non-analytic structure provides a distinct geometric realization of ‘mass’ in classical gravity. We also find that the negative mass Schwarzschild solution does not admit a similar extension within the first order theory. This is consistent with the general expectation that degenerate metric solutions associated with the Hilbert-Palatini Lagrangian formulation should satisfy the energy conditions.

The scattering of the Dirac fermions by the black-holes with spherical symmetry is studied by applying the method of partial wave analysis. The analytical expressions for the phase shifts and analytical formulas for the differential scattering cross section are written down for the fermion scattering from Schwarzschild, Reissner-Nordsrtöm and Bardeen black holes. A brief comment about the principal features of these cases is outlined.

The Kerr space-time possesses a “hidden symmetry”, which exhibits itself in an unexpected conserved quantity along geodesics known as the Carter constant. Here I report on a recent paper, where I answer the question whether this hidden symmetry can be used to formulate a conservation law for a general matter field. First, I show that there cannot exist a conserved sum of Carter constants for a matter system with momentum exchange between its components. Then, I derive a “weak” conservation law associated with the hidden symmetry and demonstrate its properties. Finally, I show how this weak conservation law and related identities can be used to detect violations of the evolution equations in numerical simulations of astrophysical processes near spinning black holes.

We consider the effects of rotations on the calculation of some thermodynamical quantities like the free energy, internal energy and entropy. In ordinary gravity, when we evaluate the density of states of a scalar field close to a black hole horizon, we obtain a divergent result which can be kept under control with the help of some standard regularization and renormalization processes. We show that when we use the Gravity’s Rainbow approach such regularization/renormalization processes can be avoided. A comparison between the calculation done in an inertial frame and in a comoving frame is presented.

The holography for rotating black holes provides a description of black hole physics in terms of a certain two-dimensional conformal field theory (CFT). The first realization of the holography for rotating black holes was proposed for extremal Kerr black hole. The proposal states that the near horizon geometry of the extremal Kerr black hole does have a dual holographic description in terms of a two-dimensional chiral CFT. The proposal has been studied and extended extensively for other extremal or near extremal rotating black holes. For all extremal and near-extremal black holes in different dimensions, the physical quantities associated to black hole (such as the entropy or scattering cross section) are in agreement with the corresponding microscopic dual quantities in CFT. In this talk, we find the explicit form of two-point function for the conformal spin-2 energy momentum operators on the near horizon of a near extremal Kerr black hole by variation of a proper boundary action. In this regard, we consider an appropriate boundary action for the gravitational perturbation of the Kerr black hole. We consider the boundary action and calculate it on-shell to find the two-point functions for the spin-2 energy momentum tensor fields, on the near horizon region of the Kerr black hole. We show that the variation of the boundary action with respect to the boundary fields yields the two-point function for the energy momentum tensor of a conformal field theory. We find agreement between the two-point function and the correlators of the dual conformal field theory to the Kerr black hole.

In this article, we will discuss a Lorentzian sector calculation of the entropy of a minimally coupled scalar field in the Schwarzschild black hole background using the brick wall model of G ’t Hooft. In the original article, the Wentzel-Kramers-Brillouin (WKB) approximation was used. In this article, we will consider the entropy for a thin shell of matter field of a given thickness surrounding the black hole horizon. The thickness is chosen to be large compared with the Planck length and is of the order of the atomic scale. The corresponding leading-order entropy of the scalar field is found to be proportional to the area of the horizon and is logarithmically divergent. Thus, the entropy of a three-dimensional system in the near-horizon region is proportional to the boundary surface. The leading order entropy is a decreasing function of the the thickness of the thin shell. This is also valid for the sub-leading terms.

The thermodynamics of a self-gravitating gas cloud of particles interacting only via their gravitational potential is an interesting problem with peculiarities arising due to the long-ranged nature of the gravitational interaction. Based on our recent work on the properties of such a configuration, we extend the system to contain a central gravitational field in which the particles are moving, to mimic the potential of a central compact object exerting an external force on the gas cloud. After an introduction to the general problem, including the aforementioned peculiarities and possible solutions, we will discuss the particular properties of the self-gravitating gas in a central field and its thermodynamic analysis.

We explore the Hawking radiation phenomenon as a tunneling process of charged spin particles through event horizons of some particular black holes. Using the semi-classical WKB approximation to the general covariant wave equations of charged particles, we evaluate the tunneling probabilities of outgoing charged particles. The Hawking temperatures corresponding to these black holes are recovered. By considering the back-reaction effects of the emitted spin particles from black holes, We calculate their corresponding quantum corrections to the radiation spectrum. It is found that this radiation spectrum is not purely thermal due to energy and charge conservation but has some corrections.

The properties of Kerr black holes (BHs)and naked singularities (NSs) are investigated by using stationary observers and their limiting frequencies. We introduce the concept of NS Killing throats and bottlenecks for slowly spinning NSs to describe the frequency of stationary observers. In particular, we show the frequency on the horizon can be used to point out a connection between BHs and NSs and to interpret the horizon in terms of frequencies. The analysis is performed on the equatorial plane of the ergoregion.

We formulate a description of 3+1 dimensional gravitational phenomena in terms of a relativistic fluid living on the 2+1 dimensional timelike boundary of an arbitrary bulk region of spacetime, called a gravitational screen. We establish a consistent dictionary between the geometric variables describing the evolution of the screen and the thermodynamic variables describing a relativistic viscous fluid, and discuss the interpretation. We also examine the construction of gravitational screens in different spacetimes and analyze the properties of the fluids they realize.

We consider spherically-symmetric black holes in semiclassical gravity. For a collapsing radiating thin shell we derive a sufficient condition on the exterior geometry that ensures that a black hole is not formed. This is also a sufficient condition for an infalling test particle to avoid the apparent horizon of an existing black hole and approach it only within a certain minimal distance. Taking the presence of a trapped region and its outer boundary — the apparent horizon — as the defining feature of black holes, we explore the consequences of their finite time of formation according to a distant observer. Assuming regularity of the apparent horizon we obtain the limiting form of the metric and the energy-momentum tensor in its vicinity that violates the null energy condition (NEC). The metric does not satisfy the sufficient condition for horizon avoidance: a thin shell collapses to form a black hole and test particles (unless too slow) cross into it in finite time. However, there may be difficulty in maintaining the expected range of the NEC violation, and stability against perturbations is not assured. On the other hand, expansion of a trapped region that was formed in a finite time of a distant observer leads to a firewall that contradicts the quantum energy inequality.

The well known Schwarzschild black hole entropy is depicted in terms of trapped gravitons within the event horizon. A discrete spectrum for the so trapped gravitons is obtained and used to calculate thermodynamic quantities. The semi-classical expression for the black hole entropy is obtained with a temperature proportional to the usual Bekenstein-Hawking one and as a result a pressure term arises in the first law of thermodynamic. My approach is an attempt to obtain the semi-classical black hole entropy in terms of degrees of freedom stored inside (but ’near’) the event horizon. Moreover, it is also shown that by modifying the internal energy by a term motivated by quantum Planckian fluctuations, a phase transition emerges during evaporation process with a vanishing specific heat at Planckian scales, thus representing the end of the evaporation process.

The following sections are included:

• Introduction
• Ansatz, asymptotic behavior and charges
• Magnetized and squashed configurations
• Supersymmetric solutions
• Conclusions
• Acknowledgments
• References

The Einstein equations describing the black-brane dynamics both in Minkowski and AdS background were recently recast in the form of coupled diffusion equations in the large-D(imension) limit. Using such results in the literature, we formulate a higher-order perturbation theory of black branes in time domain and present the general form of solutions for arbitrary initial conditions. For illustrative purposes, the solutions up to the first or second order are explicitly written down for several kind of initial conditions, such as a Gaussian wave packet, shock wave, and rather general superposed sinusoidal waves. These could be the first examples describing the non-trivial evolution of black-brane horizons in time domain. In particular, we learn some interesting aspects of black-brane dynamics such as the Gregory-Laflamme (GL) instability and non-equilibrium steady state (NESS). The formalism presented here would be applicable to the analysis of various black branes and their holographically dual field theories.

Constructing an exact correspondence between a black hole model, formed from the most simple solution of Einstein’s equations, and a particular moving mirror trajectory, we investigate a new model that preserves unitarity. The Bogoliubov coefficients in 1+1 dimensions are computed analytically. The key modification limits the origin of coordinates (moving mirror) to sub-light asymptotic speed. Effective continuity across the metric ensures that there is no information loss. The black hole emits thermal radiation and the total evaporation energy emitted is finite without backreaction, consistent with the conservation of energy.

We summarize properties of the Kerr–NUT–(A)dS spacetime in a general dimension. We also investigate a limit when several rotational parameters in the metric are set equal and study geometry of the resulting spacetime. In dimension D = 6, we found a suitable Killing vector basis, whose algebraic structure proves that symmetries of the spacetime after the limit are further enhanced.

We study static, spherically symmetric spacetimes in quadratic gravity. We show that using a conformal-to-Kundt ansatz leads to a considerable simplification of the vacuum field equations. This simplification allows us to find Schwarzschild-Bach black hole in the form of a power series expansion with coefficients given by a recurrent formula. The Schwarzschild-Bach solution is specified by two parameters, the horizon position and an additional “non-Schwarzschild parameter” b that encodes the value of the Bach tensor on the horizon. For vanishing “Bach” parameter, the Bach tensor vanishes as well and the Schwarzschild metric is recovered. The new form of the metric enables us to investigate the geometrical and physical properties of these black holes, such as tidal effects on test particles and thermodynamical quantities.

The nature of the progenitors of Type Ia supernovae (SNe Ia) remains a mystery. By performing binary population synthesis calculations, theoretical predictions for different SN Ia progenitor models, such as supernova rates, delay times, pre-explosion companion properties and early ultraviolet signatures from ejecta-companion interaction have been presented. The results are then compared with the observations to place constraints on the possible progenitor models of SNe Ia.

There has recently been an increasing interest in a possible population of type Ia supernovae (SNe Ia) triggered by helium detonation on the surface of a massive white dwarf. In this paper, we first summarize possible observational signatures of the He detonationtriggered SNe Ia, emphasizing the new diagnostics of the He detonation mode potentially seen in the SN light within the first few days since the explosion. We then argue that observational properties of a peculiar SN Ia, MUSSES1604D as discovered by the Hyper Suprime-Cam (HSC) attached with the Subaru telescope, are best explained by the He-detonation scenario. We then discuss possible origins, including the He detonation scenario, of the diversity seen in the photometric properties of SNe Ia in the first few days. While the He detonation could reproduce observational properties of a fraction of SNe Ia showing the excessive emission in the first few days, it is likely that a bulk of them are linked to a different explosion mechanism where the early excess would arise due to an extensive mixing of ⁵⁶Ni during the explosion. A combined analysis of the very early phase observations and the maximum-phase observations will be key in mapping the diverse SN Ia zoo into different populations reflecting different progenitors and/or different explosion modes.

Compact binary systems are investigated on timescales where the gravitational radiation backreaction is negligible but which is much longer than the orbital period. On this conservative timescale we use averaged equations over one orbital period removing the short time-scale modulations but keeping the secular variations. The effects of the eccentricity on the spin flip-flop is studied for equal mass binary systems. We find that eccentricity does not affect the flip-flop magnitude but it has a significant influence on its period.

We report here on a line of work that has played a key role in formally establishing and going beyond the state of the art in the effective field theory (EFT) approach and in post-Newtonian (PN) gravity. We also outline here how this comprehensive framework in fact forms the outset of a prospective rich research program, building on the public Feynman and PN technology developed.

To search for transient astrophysical neutrino sources, IceCube’s optical and X-ray follow-up program is triggered by two or more neutrino candidates arriving from a similar direction within 100 s. However, the rate of such neutrino multiplets was found to be consistent with the expected background of chance coincidences, such that the data does not provide indications for the existence of short-lived transient neutrino sources. Upper limits on the neutrino flux of transient source populations are presented in Aartsen et al. (2019) and we show here how these limits apply to the predicted neutrino emission from binary neutron star mergers.

We review some known results obtained in the context of hyperbolic scattering in a two-body system, stressing the state of the art, the main actual challenges and the related difficulties.

We review the necessary framework to study self-force effects induced by an extended body endowed with internal structure up to the quadrupole moving in a Schwarzschild black hole spacetime. The motion is described according to the Mathisson-Papapetrou-Dixon model. The metric perturbations are computed by using the Regge-Wheeler gauge. We apply this formalism to the case of Detweiler’s redshift invariant for spinning particles along circular equatorial orbits.

We review here the main advances made by using effective field theories (EFTs) in classical gravity, with notable focus on those unique to the EFTs of post-Newtonian (PN) gravity. We then proceed to overview the various prospects of using field theory to study the real-world gravitational wave (GW) data, as well as to ameliorate our fundamental understanding of gravity at all scales, by going from the EFTs of PN gravity to modern advances in scattering amplitudes, including computational techniques and intriguing duality relations between gauge and gravity theories.

We determine the binding energy, the total gravitational wave energy flux, and the gravitational wave modes for a binary of rapidly spinning black holes, working in linearized gravity and at leading orders in the orbital velocity, but to all orders in the black holes’ spins. Though the spins are treated nonperturbatively, surprisingly, the binding energy and the flux are given by simple analytical expressions which are finite (respectively third- and fifth-order) polynomials in the spins. Our final results are restricted to the important case of quasi-circular orbits with the black holes’ spins aligned with the orbital angular momentum.

There are various models that were proposed as scalar fields for inflation, some of these with an ‘attractor solutions’ to which the system evolves. For each of these models, we have a different evolution of the energy density for relativistic matter and dark matter, which were created during the reheating period, at the end of inflation in the early Universe, as a result of the ‘inflaton’ decay. Furthermore, the temperature at which the reheating takes place also depends on the type of scalar field. In this work, we consider the polynomial scalar field (chaotic inflation) of the sixth degree, and we study it with numerical methods varying the ‘free parameters’ a, b, c, obtaining the attractor behavior in particular conditions. Finally, we calculate the reheating temperature, establishing, for this case, that we are in the regime of good reheating.

I provide a brief summary of the work done on asymptotically flat black holes with synchronised hair. These black holes form families of solutions that interpolates between vacuum Kerr black holes and Bose-Einstein condensates of massive bosonic fields.

In the context of single-field inflation, the conservation of the curvature perturbation on comoving slices, ℛ_c, on super-horizon scales is one of the assumptions necessary to derive the consistency condition between the squeezed limit of the bispectrum and the spectrum of the primordial curvature perturbation. However, the conservation of ℛ_c holds only after the perturbation has reached the adiabatic limit where the constant mode of ℛ_c dominates over the other (usually decaying) mode. In this case, the non-adiabatic pressure perturbation defined in the thermodynamic sense, $\delta P_{nad}\equiv \delta P-c_w^2\delta \rho$ where $c_w^2=\dot{P}/\dot{\rho }$, usually becomes also negligible on superhorizon scales. Therefore one might think that the adiabatic limit is the same as thermodynamic adiabaticity. This is in fact not true. In other words, thermodynamic adiabaticity is not a sufflcient condition for the conservation ofℛ_c on super-horizon scales. In this paper, we consider models that satisfy δP_nad = 0 on all scales, which we call global adiabaticity (GA), which is guaranteed if $c_w^2=c_s^2$, where c_s is the phase velocity of the propagation of the perturbation. A known example is the case of ultra-slow-roll(USR) inflation in which$c_w^2=c_s^2=1$. In order to generalize USR we develop a method to find the Lagrangian of GA K-inflation models from the behavior of background quantities as functions of the scale factor. Applying this method we show that there indeed exists a wide class of GA models with $c_w^2=c_s^2$, which allowsℛ_c to grow on superhorizon scales, and hence violates the non-Gaussianity consistency condition.

In this work, we discuss whether the new ekpyrotic scenario can be embedded into ten-dimensional supergravity. We use that the scalar potential obtained from flux compactifications of type II supergravity with sources has a universal scaling with respect to the dilaton and the volume mode. Similar to the investigation of inflationary models, we find very strong constraints ruling out ekpyrosis from analysing the fast-roll conditions. We conclude that flux compactifications tend to provide potentials that are neither too flat and positive (inflation) nor too steep and negative (ekpyrosis).

We derive a general equation for the evolution of the curvature perturbation on comoving slices ℛ_c in the presence of anisotropy and non-adiabaticity in the energy-momentum tensor of matter fields. The equation is obtained by manipulating the perturbed Einstein equations in the comoving slicing. It could be used to study the evolution of perturbations for a system with an anisotropic energy-momentum tensor, such as in the presence of a vector field or in the presence of non-adiabaticity, such as in a multi-field system.

We find two distinct families of new charged boson star solutions of a complex scalar field coupled non-minimally to gravity by a “John-type” term of Horndeski theory. The end points of one of the branches are extremal Reissner-Nordström black hole solutions.

The high-redshift 21-cm signal of neutral hydrogen is expected to be a sensitive probe of primordial star formation as well as of the heating and ionization histories of the Universe. The recent tentative detection by the EDGES Low-Band of the cosmological 21-cm signal, if confirmed, is the first ever signature from the dawn of star formation. However, the magnitude and the shape of this signal are incompatible with standard astrophysical predictions, requiring either colder than expected gas, or an excess radio background above the Cosmic Microwave Background (CMB) radiation. Here we provide a brief overview of 21-cm cosmology, the status of the global 21-cm experiments and proposed theoretical explanations for the EDGES detection.

The rotation of the galactic objects has been seen by asymmetric Doppler shift in the CMB data. Molecular hydrogen clouds at virial temperature may contribute to the galactic halo dark matter and they might be the reason for the observed rotational asymmetry in the galactic halos. We present a method to constrain the parameters of these virial clouds given that they are composed of a single fluid. The method is such that it should be possible to extend it to more than one fluid.

The boosting effects induced by the peculiar motion of an observer with respect to the Cosmic Microwave Background (CMB) rest frame can be explored to analyze the frequency dependence of the dipole. The improvements achievable with future CMB missions on our knowledge of CMB spectral distortions and Cosmic Infrared Background spectrum are discussed considering realistic uncertainties in relative calibration and foreground subtraction.

The Planck mission has clearly demonstrated that, although not specifically designed for the observation of extragalactic sources, the space-borne experiments aimed at investigating the Cosmic Microwave Background (CMB) have the potential to bring breakthrough science also in this field. One example is the detection of high-z galaxies with extreme gravitational amplifications. The combination of flux boosting and of stretching of the images has allowed the investigation of the structure of galaxies at z ⋍ 3 with the astounding spatial resolution of ⋍ 60 pc. Another example is the detection of proto-clusters of dusty galaxies at high z, when they may not yet possess the hot intergalactic medium allowing their detection in X-rays or via the Sunyaev-Zeldovich effect.

We study the effects of a uniform magnetic field on the evolution of cosmological perturbations, in a full relativistic framework, considering the effects of anisotropies. We take advantage of the synchronous gauge to simplify the equations. We study both super-horizon scales in radiation dominated universe and sub-horizon scales in both a full relativistic framework and the Newtonian limit in case of adiabatic sound speed.

In this talk I will review the current status of the constraints on the neutrino properties from cosmological measurements, with a particular focus on their mass and effective number. I will also discuss the existing tensions within the context of the ΛCDM model, including the discrepancies on the Hubble parameter and on the matter fluctuations at small scales, and how neutrinos could help to alleviate the aforementioned problems.

We derive new constraints on the Hubble parameter H₀ using the available data on H(𝓏) from cosmic chronometers (CCH), and the Hubble rate data points from the supernovae of Type Ia (SnIa) of the Pantheon compilation and the Hubble Space Telescope (HST) CANDELS and CLASH Multy-Cycle Treasury (MCT) programs. We employ two alternative techniques, Gaussian Processes (GPs) and the Weighted Polynomial Regression (WPR) method, to reconstruct the Hubble function, determine the derived values of H₀, and compare them with the local HST measurement provided by Riess et al. (2018), $H_0^{HST}=\left(73.48\pm 1.66\right)\text{km/s/Mpc}$, and with the Planck+ΛCDM value, $H_0^{P18}=\left(66.88\pm 0.92\right)\text{km/s/Mpc}$,. With GPs we obtain H₀ = (67.99 ± 1.94) km/s/Mpc and with the WPR method H₀ = (68.90 ± 1.96) km/s/Mpc. Both are fully compatible at < 1σ c.l., and also with $H_0^{P18}$. In contrast, they are in ∼ 2σ tension with $H_0^{HST}$.

I review briefly three problems where tensions between predictions based on numerical simulations of the Lambda-CDM prototype and observations at small (galactic) scales occur. These include (i) the core-cusp problem on the galactic profiles, (ii) the missing satellite problem, and the (ii) too-big-to-fail problem. I explain what these problems are and present potential resolutions, first through some astrophysical mechanisms, which however, as I argue, fail to alleviate completely the problems, at least currently. Then, I discuss fundamental modifications of the Lambda-CDM model, through the inclusion of self-interacting dark matter (SIDM). I argue that a simple model of SIDM, with (warm) self-interacting right-handed neutrinos (RHN), that exist in minimal extensions of the Standard model of particle physics, appears promising in providing a resolution of the aforementioned “small-scale-Cosmology crisis”, in particular the core-cusp problem, and an observationally consistent description of the core-halo structure in galaxies.

The goal of this short report is to summarise some key results based on our previous works on model independent tests of gravity at large scales in the Universe, their connection with the properties of gravitational waves, and the implications of the recent measurement of the speed of tensors for the phenomenology of general families of gravity models for dark energy.

Multipole vectors and pseudo entropies provide powerful tools for a numerically fast and vivid investigation of possible statistically anisotropic, resp. non-Gaussian signs in CMB temperature fluctuations. After reviewing and linking these two conceptions we compare their application to data analysis using the Planck 2015 NILC full sky map.

We present a preliminary analysis of the optical system of the STRIP instrument of the Large Scale Polarization (LSPE) experiment, which aims at polarization measurements of the Cosmic Microwave Background on large angular scales. STRIP will observe approximately 25% of the Northern sky from the Observatorio del Teide in Tenerife, using an array of forty-nine coherent polarimeters at 43 GHz (Q-band), coupled to a 1.5 m fully rotating crossed-Dragone telescope. An additional frequency channel with six-elements at 95 GHz (W-band) will be exploited as an atmospheric monitor.

Non-idealities in the optical system may introduce limitations in achieving high precision measurements, if not well understood and controlled. For this reason, we studied the optical design of STRIP, its characteristics in terms of performance on angular resolution, sidelobes, main beam symmetry, polarization purity and feedhorns orientation, by means of electromagnetic simulations.

One of the main goals of modern cosmology is to probe inflationary theories by looking on the imprint of primordial gravitational waves in the cosmic microwave background (CMB) polarization field. Future CMB experiments face the great challenge to search for this primordial B-mode signal. However, the CMB sky is also filled with secondary B-modes, including CMB lensing and astrophysical foregrounds. Extracting the CMB B-mode polarization from astrophysical contaminations is a primordial task towards detection of the primordial signal. We use the analytical method of blind separation (ABS) proposed by Zhang, P., et al. (2019) to reconstruct the CMB B-mode power spectrum in the presence of foregrounds and white noise considering a full sky analysis for r = 0.

Cosmic strings in the early universe have received revived interest in recent years. In this work we derive these structures as topological defects from singular distributions of the quintessence field of dark energy. Emphasis is placed on the topological charge of tangled cosmic strings, which originates from the Hopf mapping degree and is a Chern-Simons type action possessing strong inherent tie to knot topology. It is shown that the HOMFLYPT (Jones) polynomial can be constructed in terms of this charge, serving as a topological invariant much stronger than the traditional Gauss linking numbers in characterizing string topology. This method induces applications in two aspects. One is to search a tool to measure the cascade of decreasing topological complexity and that of decreasing energy/entropy. The other is arousing a promising mathematical approach for the study of physical breaking-reconnection processes of tangled cosmic strings.

I investigate the relativistic mechanics of an extended “cable” in an arbitrary static, spherically symmetric spacetime. Such hypothetical bodies have been proposed as tests of energy and thermodynamics: by lowering objects toward a black hole, scooping up Hawking radiation, or mining energy from the expansion of the universe. I review existing work on stationary cables, which demonstrates an interesting “redshift” of tension, and extend to a case of rigid motion. By using a partly restrained cable to turn a turbine, the energy harvested is up to the equivalent of the cable’s rest mass, concurring with the quasistatic case. Still, the total Killing energy of the system is conserved.

Cosmic topological defects possibly formed during phase transitions in the very early universe and are theoretically well-motivated. Cosmic strings (CSs) would leave distinct imprints on CMB fluctuations. We apply certain topological and geometrical measures in a multi-scale edge-detection algorithm to CMB maps with contributions from CS network to assess the capability of the CS footprints. On the noiseless sky maps with an angular resolution of 0.9′, we show that our pipeline is capable of detecting CSs with Gμ as low as Gμ > 4.3 × 10^-10. We also explore two powerful tree-based machine learning algorithms to perform feature importance analysis. This analysis would improve future CS searches to focus on the most significant and informative features. Our machine-learning algorithm can detect CSs with Gμ > 2.1 × 10^-10 at 3σ level, for a noise-less experiment and angular resolution of 0.9′.

Topological defects formed in the early stages of our universe can play a crucial role in understanding anisotropic deviations of the Friedmann Lemâitre Robertson Walker model we observe today. These defects are the result of phase transitions associated with spontaneous symmetry breaking in gauge theories at the grand unification energy scale. The most interesting defects are cosmic strings, vortex-like structures in the famous gauged U(1) abelian Higgs model with a “Mexican-hat” potential. Other defects, such as domain walls and monopoles are probably ruled out, because they should dominate otherwise the energy density of our universe. This local gauge model is the basis of the standard model of particle physics, where the Higgs-mechanism provides elementary particles with mass. It cannot be a coincidence that this model also explains the theory of superconductivity. The decay of the high multiplicity (n) super-conducting vortex into a lattice of n vortices of unit magnetic flux is energetically favourable and is experimentally confirmed. It explains the famous Meissner effect. This process could play an essential role by the entanglement of cosmic strings just after the symmetry breaking. The stability of the lattice depends critically on the parameters of the model, especially when gravity comes into play. The questions is how the imprint of the cosmic strings could be observed at present time. Up to now, no evidence is found. The recently found alignment of the spinning axes of quasars in large quasar groups on Mpc scales, could be a first indication of the existence of these cosmic strings. The temporarily broken axial symmetry will leave an imprint of a preferred azimuthal-angle on the lattice. This effect is only viable when a scaling factor is introduced. This can be realized in a warped five dimensional model. The warp factor plays the role of a dilaton field on an equal footing with the Higgs field. The resulting field equations can be obtained from a conformal invariant model. Conformal invariance, the missing symmetry in general relativity, will then spontaneously be broken, just as the Higgs field. The dilaton field, or equivalently, the warp factor, could also contribute to the expansion of the universe as it can act as a dark energy term coming from the bulk spacetime. It makes the cosmic string temporarily super-massive. This process could solve the cosmological constant and hierarchy problem. It is conjectured that the dilaton field has a dual meaning. At very early times, when the dilaton field approaches zero, it describes the small-distance limit of the model, while at later times it is a warp (or scale) factor that determines the dynamical evolution of the universe. When more data of quasars of high redshift will become available, one could prove that the alignment emerged after the symmetry breaking scale and must have a cosmological origin. The effect of the warp factor on the second-order perturbations could also be an indication of the existence of large extra dimensions.

We examine a dark-energy equation of state. From there, we link early-universe graviton production by varying the DE equation from –1 to 1 with a Kaluza–Klein treatment of reacceleration and comment on how modification of gravitational $\frac{1}{r}$ potentials and the reacceleration of the universe also bridge between the first and second parts of this document, in terms DE physics and gravitons, as well as changing Q(z) reacceleration behavior. We close with a suggestion on redoing initial contributions to DE.

A naive five-dimensional model simultaneously explains dark energy and the flat rotation curves of galaxies and enhanced gravitational lensing usually attributed to dark matter. An additional (fifth) dimension is invoked which corresponds to the radius of curvature of four-dimensional space-time and does not represent a degree of freedom of motion. The universe so modeled has two modes of expansion: that of three-dimensional space and that of the fifth dimension itself, where the latter has the characteristics partly of space and partly of time. The boundary between four-dimensional space-time and the fifth dimension is modeled by contours along which energy is conserved. The model is able to reproduce: (i) the observed relationship between distance modulus and red shift for Type 1a supernovae; (ii) the Tully-Fisher relationship; and (iii) gravitational lensing effects beyond General Relativity for galaxies and clusters of galaxies.

In this manuscript, we will discuss the construction of a theory of gravity with nonmetricity and general affine connections. We will consider a simple potential formalism with symmetric affine connections and symmetric Ricci tensor. Corresponding affine connections introduce two massless scalar fields. One of these fields contributes a stress-tensor with opposite sign to the sources of Einstein’s equation when we state the equation using the Levi-Civita connections. This means we have a massless scalar field with negative stress-tensor in the familiar Einstein equation. These scalar fields can be useful to explain dark energy and inflation. These fields bring us beyond strict local Minkowski geometries.

We consider a model based on p-form kinetic Lagrangians in the context of dark energy. The Lagrangian of the model is built with kinetic terms of the field strength for each p-form coupled to a scalar field ϕ through a kinetic function. We assume that this scalar field is responsible for the present accelerated expansion of the Universe. Since we are interested in cosmological applications, we specialize the analysis to a 4-dimensional case, using an anisotropic space-time. By studying the dynamical equations, we investigate the evolution of the dark energy density parameter, the effective equation of state and the shear induced by the anisotropic configuration.

In order to reconcile the quantum mechanics and general relativity, the equivalence principle of quantum gravity is introduced for extending the equivalence principle of general relativity to the observer frames of reference which are in quantum mechanical motions. The equivalence principle of quantum gravity is that the laws of physics must be of such a nature that they apply to systems of reference in any kind of motions, both classical and quantum mechanical. Under such principle, the quantum gravity should be formulated in the quantum space-time-matter space with local conformal symmetry and the mathematical expressions for the cosmological constant as well as the masses of fundamental particles can be found by the theory.

In this work, we study the F (R) gravity with f -essence for the flat and homogeneous Friedman-Robertson-Walker universe. For this model, we have presented the point-like Lagrangian and the corresponding field equations. To describe the dynamics of the universe, we have investigated some cosmological solutions for K, F and h functions. It is shown that these solutions describe the late time accelerated expansion of the Universe.

In this paper, we explore f (T) gravity which non-minimally coupled to fermionic fields in (2+1) spatially flat Friedmann-Robertson-Walker (FRW) dimensions. Friedmann equations, equations for fermionic fields are derived. Forms of gravitational coupling, self-interaction potential and f (T) gravity are reconstructed by Noether symmetry approach for the point-like Lagrangian. Cosmological solution of model which corresponding to the late-time accelerating expansion are obtained.

We perform a forecast analysis on the ability of future baryonic acoustic oscillation (BAO) and cosmic microwave background (CMB) experiments in constraining 3 specific interacting dark energy models using the well known Fisher-matrix formalism. In addition to a future ground-based CMB experiment, we consider a Euclid-like experiment, which is supposed to put tight constraints on the dark sector parameters. In the interacting dark energy scenario, a coupling between dark matter and dark energy modifies the conservation equations such that the fluid equations for both constituents are conserved as the total energy density of the dark sector. In this context, we consider three phenomenological models which have been deeply investigated in literature in the past years. We find that the combination of both CMB and BAO can break degeneracies among the parameters for every studied model. We found powerful constraints on, for example, the coupling constant when comparing it with present limits for two of the models, and their future statistical 3-σ bounds could potentially exclude the null interaction for the combination of probes that is considered.

By using a cosmographic analysis of the redshift data of type Ia supernovae, we are able to get the expansion of the scale factor, obtaining the current values of the Hubble, deceleration, jerk and snap parameters. Our data is then used to compare the fitness of various proposed alternative cosmological models. Since our method assumes only the validity of general relativity at the cosmic scale, along with the isotropy and homogeneity of the universe, they are very useful for comparison between different cosmological models, including the fitness of ΛCDM model. Our method is based on the order expansion of the scale factor present in the FRW metric and using a Monte Carlo integration to find the best fit order parameters of the scale factor to reproduce the observed data, we make use of parallel paradigm to improve the computational time behind the model. We find the known result of an accelerated expansion of the universe. With access to better measurements of type Ia supernovae redshifts and more data, the cosmographic results will be significantly improved.

Scalar fields which are favorite among the possible candidates for the dark energy usually have degenerate minima at ±ϕ_min. In the presented work, we discuss a two Higgs doublet model with the non-degenerate vacuum named inert uplifted double well type two-Higgs doublet model (UDW-2HDM) for the dark energy. It is shown that when the both Higgs doublets lie in their respective true minima then one Higgs doublet can cause the current accelerated expansion of the Universe.

We find that having the scale factor close to zero due to a given magnetic field value in an early-universe magnetic field affects how we would interpret Mukhanov’s chapter on self-reproduction of the universe. A stronger early-universe magnetic field suggests a greater likelihood of production of about 20 new domains of size $\frac{1}{H}$, with H the early-universe Hubble constant per Planck time interval in evolution. Fluctuations in the Hubble expansion parameter, H, may affect structure. Finally, α in a gravitational potential is proportional to r^−α. This adjustment affects the three-body problem.

Calculations of the flux power spectrum of the Lyman α forest are performed as a means to quantify the possible effects of time-dependent dark energy. We use a parameterized version of the time-dependent dark energy equation of state consistent with the Planck analysis. We have run high-resolution, large-scale cosmological simulation with a modified version of the publicly available SPH code GADGET-2. These simulations were used to extract synthetic Lyman α forest spectra. These were then used to simulate the flux power spectrum at various observed quasar redshifts. We conclude that the effect of time-dependent dark energy on the flux power spectrum is of marginal statistical significance compared to the intrinsic cosmic variance.

The recent analysis of low-redshift supernovae (SN) has increased the apparent tension between the value of H₀ estimated from low and high redshift observations such as the cosmic microwave background (CMB) radiation. At the same time other observations have provided evidence of the existence of local radial inhomogeneities extending in different directions up to a redshift of about 0.07. About 40% of the Cepheids used for SN calibration are directly affected because are located along the directions of these inhomogeneities. We compute with different methods the effects of these inhomogeneities on the low-redshift luminosity and angular diameter distance using an exact solution of the Einstein’s equations, linear perturbation theory and a low-redshift expansion. We confirm that at low redshift the dominant effect is the non relativist Doppler redshift correction, which is proportional to the volume averaged density contrast and to the comoving distance from the center. We derive a new simple formula relating directly the luminosity distance to the monopole of the density contrast, which does not involve any metric perturbation. We then use it to develop a new inversion method to reconstruct the monopole of the density field from the deviations of the redshift uncorrected observed luminosity distance respect to the ΛCDM prediction based on cosmological parameters obtained from large scale observations.

The inversion method confirms the existence of inhomogeneities whose effects were not previously taken into account because the 2M ++ density field maps used to obtain the peculiar velocity for redshift correction were for 𝓏 ≤ 0.06, which is not a sufficiently large scale to detect the presence of inhomogeneities extending up to 𝓏 = 0.07. The inhomogeneity does not affect the high redshift luminosity distance because the volume averaged density contrast tends to zero asymptotically, making the value of $H_0^{CMB}$ obtained from CMB observations insensitive to any local structure. The inversion method can provide a unique tool to reconstruct the density field at high redshift where only SN data is available, and in particular to normalize correctly the density field respect to the average large scale density of the Universe.

We investigate the relativistic corrections to the standard model of formation of large scale structures. In matter domination and in the Poisson gauge, we use the weak- field approximation which allows to keep compact expressions even for the one-loop bispectrum. Whereas in the Newtonian limit, the choice of gauge is marginally important as all gauge coincides, when relativistic corrections are taken into account, it matters as a change of gauge may induce a change of gravitational potential and introduce fictitious modes in the finial result for the power spectrum. It is precisely what happens in the example presented in this talk as the equivalence principle is not fulfilled in the Poisson gauge and the cancellation of the IR divergence at one-loop does not occur. We will discuss how other choices of gauge may solve this issue.