International Journal of Modern Physics D

The theory of cosmological perturbations is a well-elaborated field and has been successfully applied, e.g. to model the structure formation in our universe and the prediction of the power spectrum of the cosmic microwave background. To deal with the diffeomorphism invariance of general relativity, one generally introduces combinations of the metric and matter perturbations, which are gauge invariant up to the considered order in the perturbations. For linear cosmological perturbations, one works with the so-called Bardeen potentials widely used in this context. However, there exists no common procedure to construct gauge invariant quantities also for higher-order perturbations. Usually, one has to find new gauge invariant quantities independently for each order in perturbation theory. With the relational formalism introduced by Rovelli and further developed by Dittrich and Thiemann, it is in principle possible to calculate manifestly gauge invariant quantities, that is quantities that are gauge invariant up to arbitrary order once one has chosen a set of so-called reference fields, often also called clock fields. This article contains a review of the relational formalism and its application to canonical general relativity following the work of Garcia, Pons, Sundermeyer and Salisbury. As the starting point for our application of this formalism to cosmological perturbation theory, we also review the Hamiltonian formulation of the linearized theory for perturbations around FLRW spacetimes. The main aim of our work will be to identify clock fields in the context of the relational formalism that can be used to reconstruct quantities like the Bardeen potential as well as the Mukhanov–Sasaki variable. This requires a careful analysis of the canonical formulation in the extended ADM-phase-space where lapse and shift are treated as dynamical variables. The actual construction of such observables and further investigations thereof will be carried out in our companion paper.

We have recently proposed a new action principle for combining Einstein equations and the Dirac equation for a point mass. We used a length scale $L_{\mathrm{\text{CS}}}$, dubbed the Compton–Schwarzschild length, to which the Compton wavelength and Schwarzschild radius are small mass and large mass approximations, respectively. Here, we write down the field equations which follow from this action. We argue that the large mass limit yields Einstein equations, provided we assume the wave function collapse and localization for large masses. The small mass limit yields the Dirac equation. We explain why the Kerr–Newman black hole has the same gyromagnetic ratio as the Dirac electron, both being twice the classical value. The small mass limit also provides compelling reasons for introducing torsion, which is sourced by the spin density of the Dirac field. There is thus a symmetry between torsion and gravity: torsion couples to quantum objects through Planck’s constant $\hslash$ (but not $G$) and is important in the microscopic limit. Whereas gravity couples to classical matter, as usual, through Newton’s gravitational constant $G$ (but not $\hslash$), and is important in the macroscopic limit. We construct the Einstein–Cartan–Dirac equations which include the length $L_{\mathrm{\text{CS}}}$. We find a potentially significant change in the coupling constant of the torsion driven cubic nonlinear self-interaction term in the Dirac–Hehl–Datta equation. We speculate on the possibility that gravity is not a fundamental interaction, but emerges as a consequence of wave function collapse, and that the gravitational constant maybe expressible in terms of Planck’s constant and the parameters of dynamical collapse models.

In this study, we discuss coexistence of the early-time inflation and the late-time acceleration of the universe in the context of the theory of $F(G,T)$ gravity with scalar field which is minimally coupled with the gravity, where $G$ is the gauss bonnet invariant and $T$ is the trace of energy–momentum tensor (EMT). We reconstruct the Friedmann equation (FE) and then search for the real value of a particular model $F(G,T)=f(G)+\beta T^n$, where $\beta$ and $n$ are real constants. A Gauss–Bonnet system (GBS) for viable cosmologies arising from the matter-source term $\beta T^n$ and the scalar field, is obtained. We find that the case $n<0$ together with $f(G)\sim G^n$ in the system gives the late-time cosmic acceleration while the source term $\beta T^n$ acts as a quintessence type of dark energy. On the other hand, the general entropy expression of the universe is obtained by making use of the first law of thermodynamics (FLT) method. After theoretically analyzing the inflation in the entropy frame, we find a new condition $0<\sigma <\frac{1}{2}$ with $f(G)\sim G^{\sigma }$ in the system. Then, from the observational analysis of inflation, the spectral index parameter and the scalar-tensor ratio are calculated under the new condition. In brief, we obtain a viable cosmological system arising from some modifications such as the scalar field and the source term, which can unify the early inflation and the late-time cosmic acceleration besides the deceleration regions of the universe.

In this work, we study the cosmological attractor models of inflation in connection with certain scalar–tensor theories of gravity, e.g. $f(R)$ gravity and Brans–Dicke theory. For some particular choices of the functional degrees of freedom in these theories, one obtains Starobinsky-like predictions in the ($n_s-r$) observable plane. We have demonstrated that these choices in the Lagrangian density of certain $f(R)$ and Brans–Dicke theories fulfil the condition of the cosmological attractors. That explains why known predictions of $f(R)$ and Brans–Dicke theories in certain cases appear to be the predictions of the much discussed attractor theories. In addition, we did an analysis showing how the predictions of an attractor model are preserved with respect to the variation in the functional freedom of the theory.

We show that a generalized Dirac structure survives beyond the linear regime of the low-energy dispersion relations of graphene. A generalized uncertainty principle of the kind compatible with specific quantum gravity scenarios with a fundamental minimal length (here graphene lattice spacing) and Lorentz violation (here the particle/hole asymmetry, the trigonal warping, etc.) is naturally obtained. We then show that the corresponding emergent field theory is a table-top realization of such scenarios, by explicitly computing the third-order Hamiltonian, and giving the general recipe for any order. Remarkably, our results imply that going beyond the low-energy approximation does not spoil the well-known correspondence with analog massless quantum electrodynamics phenomena (as usually believed), but rather it is a way to obtain experimental signatures of quantum-gravity-like corrections to such phenomena.

We generalize the idea of quantum clock time to quantum spacetime reference frame via physical realization of a reference system by quantum rulers and clocks. Omitting the internal degrees of freedom (such as spins) of the physical rulers and clocks, only considering their metric properties, the spacetime reference frame is described by a bosonic nonlinear sigma model (NLSM). We study the quantum behavior of the system under approximations, and obtain (1) a cosmological constant valued $(2/\pi ){\rho }_{c0}$ (${\rho }_{c0}$ the critical density at near current epoch) which is very close to the observations; (2) an effective Einstein–Hilbert term; (3) the ratio of variance to mean-squared of spacetime interval tends to a universal constant $2/\pi$ in the infrared region. This effect is testable by observing a linear dependence between the inherent quantum variance and mean-squared of the redshifts from cosmic distant spectral lines. The proportionality is expected to be the observed percentage of the dark energy. The equivalence principle is also generalized to the quantum level.

Current study highlights the physical characteristics of charged anisotropic compact stars by exploring some exact solutions of modified field equations in $f(R,G)$ gravity. A comprehensive analysis is performed from the obtained solutions regarding stability, energy conditions, regularity, sound velocity and compactness. These solutions can be referred to model the compact celestial entities. In particular, a compact star named, $\mathrm{\text{Her}}X-1$ has been modeled which indicates that current solution fits and is in conformity to the observational data as well. A useful and interesting fact from this model arises that relative difference between two forces of anisotropic pressure and electromagnetic force may occur inside the aforementioned compact star. This is another mechanism which is essential for stability of the compact object and prevent stellar object to annihilate.

We present an elastic constitutive model of gravity where we identify physical space with the mid-hypersurface of an elastic hyperplate called the “cosmic fabric” and spacetime with the fabric’s worldvolume. Using a Lagrangian formulation, we show that the fabric’s behavior as derived from Hooke’s Law is analogous to that of spacetime per the Field Equations of General Relativity (GR). The study is conducted in the limit of small strains, or analogously, in the limit of weak and nearly static gravitational fields. The Fabric’s Lagrangian outside of inclusions is shown to have the same form as the Einstein–Hilbert Lagrangian for free space. Properties of the fabric such as strain, stress, vibrations and elastic moduli are related to properties of gravity and space, such as the gravitational potential, gravitational acceleration, gravitational waves and the energy density of free space. By introducing a mechanical analogy of GR, we enable the application of Solid Mechanics tools to address problems in Cosmology.

We analyze a fully geometric approach to dark energy in the framework of $F(R,{𝒢})$ theories of gravity, where $R$ is the Ricci curvature scalar and ${𝒢}$ is the Gauss–Bonnet topological invariant. The latter invariant naturally exhausts, together with $R$, the whole curvature content related to curvature invariants coming from the Riemann tensor. In particular, we study a class of $F(R,{𝒢})$ models with power law solutions and find that, depending on the value of the geometrical parameter, a shift in the anisotropy peaks position of the temperature power spectrum is produced, as well as an increasing in the matter power spectrum amplitude. This fact could be extremely relevant to fix the form of the $F(R,{𝒢})$ model. We also perform an MCMC analysis using both Cosmic Microwave Background data by the Planck (2015) release and the Joint Light-Curve Analysis of the SNLS–SDSS collaborative effort, combined with the current local measurements of the Hubble value, $H_0$, and galaxy data from the Sloan Digital Sky Survey (BOSS CMASS DR11). We show that such a model can describe the CMB data with slightly high $H_0$ values, and the prediction on the amplitude matter spectrum value is proved to be in accordance with the observed matter distribution of the universe. At the same time, the value constrained for the geometric parameter implies a density evolution of such a component that is growing with time.

Classical equivalence between Jordan’s and Einstein’s frame counterparts of $F(R)$ theory of gravity has recently been questioned, since the two produce different Noether symmetries, which could not be translated back and forth using transformation relations. Here we add the Hamiltonian constraint equation, which is essentially the time–time component of Einstein’s equation, through a Lagrange multiplier to the existence condition for Noether symmetry and show that all the three different canonical structures of $F(R)$ theory of gravity, including the one which follows from Lagrange multiplier technique, admit each and every available symmetry independently. This establishes classical equivalence.

We deal with a dynamical mechanism in which a large cosmological constant, as suggested by inflationary scenarios, decays due to expansion of the universe. This mechanism has its origin in the gravitational coupling of the vacuum density. We assume that the vacuum couples anomalously to gravity that is the metric tensor that appears the gravitational part is not the same as that appears the matter part as suggested by weak equivalence principle. Instead, the two metric tensors are taken to be conformally related. We show that this provides a dynamical mechanism which works during expansion of the universe. We also consider some observational consequences of such a gravitational model.

Warm generalized Chaplygin gas inflation is being studied by assuming power-law plateau and inverse symmetric potentials with standard scalar field model. We consider strong dissipative regime with generalized dissipative coefficient and extract the various inflationary parameters such as scalar power spectrum, spectral index, tensor-to-scalar ratio and running of spectral index. It is found that both inflationary potentials favor the strong dissipative regime. Also, we construct the $n_s$–${\alpha }_s$ (running of spectral index versus spectral index) and $n_s$–$r$ (tensor-to-scalar ratio versus spectral index) planes and found that the trajectories of these planes favor WMAP 7 $+$ WMAP 9 and latest Planck data.

We investigate particle motion and collisions in the vicinity of rotating black holes immersed in combined cosmological quintessential scalar field and external magnetic field. The quintessential dark-energy field governing the spacetime structure is characterized by the quintessential state parameter ${\omega }_q\in (-1;-1/3)$ characterizing its equation of state, and the quintessential field-intensity parameter $c$ determining the static radius where the black hole attraction is just balanced by the quintessential repulsion. The magnetic field is assumed to be test field that is uniform close to the static radius, where the spacetime is nearly flat, being characterized by strength $B$ there. Deformations of the test magnetic field in vicinity of the black hole, caused by the Ricci non-flat spacetime structure are determined. General expression of the center-of-mass energy of the colliding charged or uncharged particles near the black hole is given and discussed in several special cases. In the case of nonrotating black holes, we discuss collisions of two particles freely falling from vicinity of the static radius, or one such a particle colliding with charged particle revolving at the innermost stable circular orbit. In the case of rotating black holes, we discuss briefly particles falling in the equatorial plane and colliding in close vicinity of the black hole horizon, concentrating attention to the interplay of the effects of the quintessential field and the external magnetic field. We demonstrate that the ultra-high center-of-mass energy can be obtained for black holes placed in an external magnetic field for an infinitesimally small quintessential field-intensity parameter $c$; the center-of-mass energy decreases if the quintessential field-intensity parameter $c$ increases.

In this paper, we present a strange stellar model using Tolman $V$-type metric potential employing simplest form of the MIT bag equation of state (EOS) for the quark matter. We consider that the stellar system is spherically symmetric, compact and made of an anisotropic fluid. Choosing different values of $n$ we obtain exact solutions of the Einstein field equations and finally conclude that for a specific value of the parameter $n=1/2$, we find physically acceptable features of the stellar object. Further, we conduct different physical tests, viz., the energy condition, generalized Tolman–Oppeheimer–Volkoff (TOV) equation, Herrera’s cracking concept, etc., to confirm the physical validity of the presented model. Matching conditions provide expressions for different constants whereas maximization of the anisotropy parameter provides bag constant. By using the observed data of several compact stars, we derive exact values of some of the physical parameters and exhibit their features in tabular form. It is to note that our predicted value of the bag constant satisfies the report of CERN-SPS and RHIC.

We study a classical bilocal field theory perturbatively up to second-order. The chosen theory is the simplest which incorporates action-at-a-distance, while keeping nonlocal effects short-ranged. We show that the new degrees of freedom introduced by bilocality can be interpreted as gravitational degrees of freedom in the following sense: solutions of the bilocal system at linear and second-orders contain as a subset, gravitational perturbations (spacetime fluctuations) also to that order. In other words, gravity can be thought to originate in a bilocal field theory. We examine potential implications.