International Journal of Modern Physics D

In this paper, we summarize some of the main observational challenges for the standard Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model and describe how results recently presented in the parallel session “Large-scale Structure and Statistics” (DE3) at the “Fourteenth Marcel Grossman Meeting on General Relativity” are related to these challenges.

Boost modes ${\mathrm{\Psi }}_{\varkappa }(x)$ are eigenfunctions of the Lorentz transformations generator in two-dimensional (2D) Minkowski space (MS). We demonstrate and discuss deep interrelation between the boost modes and the field correlators, also known as Wightman functions. In the case of a massive scalar field, the boost modes, as functions of the spectral parameter $\varkappa$, contain the Dirac delta-function singularity $\delta (\varkappa )$ at the light cone. The zero boost mode coincides up to a constant factor with the Wightman function. The light cone singularity of boost modes for a fermion field is stronger. For this case, they contain the Gelfand $\delta$-function of complex argument $\delta (\varkappa \pm i/2)$, while the Wightman function components coincide with analytical continuation of the boost modes set towards the spectral values $\varkappa =\mp i/2$. We argue that due to the discovered properties of the boost modes the so-called Unruh modes, which are at the core of the Unruh effect derivation, do not constitute a complete set in MS and thus cannot be used for quantization of neither scalar, nor fermion field. Finally, we discuss boost modes for the case of the constant electric background and rederive the well-known result for spontaneous pair creation rate. Solution of this problem in the boost modes representation reveals distinctions between the Unruh problem and the effect of pair creation by an electric field in vacuum.

We review pedagogically some of the basic essentials regarding recent results intertwining boundary conditions, the algebra of constraints and hidden symmetries in quantum cosmology. They were extensively published in Refs. [S. Jalalzadeh, S. M. M. Rasouli and P. V. Moniz, Phys. Rev. D 90 (2014) 023541, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 89 (2014), S. Jalalzadeh, T. Rostami and P. V. Moniz, Eur. Phys. J. C 75 (2015) 38, arXiv:gr-qc/1412.6439 and T. Rostami, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 92 (2015) 023526, arXiv:gr-qc/1507.04212], where complete discussions and full details can be found. More concretely, in Refs. [S. Jalalzadeh, S. M. M. Rasouli and P. V. Moniz, Phys. Rev. D 90 (2014) 023541, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 89 (2014) and S. Jalalzadeh, T. Rostami and P. V. Moniz, Eur. Phys. J. C 75 (2015) 38, arXiv:gr-qc/1412.6439] it has been shown that specific boundary conditions can be related to the algebra of Dirac observables. Moreover, a process afterwards associated to the algebra of existent hidden symmetries, from which the boundary conditions can be selected, was introduced. On the other hand, in Ref. [T. Rostami, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 92 (2015) 023526, arXiv:gr-qc/1507.04212] it was subsequently argued that some factor ordering choices can be extracted from the hidden symmetries structure of the minisuperspace model.

In Refs. [S. Jalalzadeh, S. M. M. Rasouli and P. V. Moniz, Phys. Rev. D 90 (2014) 023541, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 89 (2014), S. Jalalzadeh, T. Rostami and P. V. Moniz, Eur. Phys. J. C 75 (2015) 38, arXiv:gr-qc/1412.6439 and T. Rostami, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 92 (2015) 023526, arXiv:gr-qc/1507.04212], we proceeded gradually towards less simple models, ranging from a FLRW model with a perfect fluid [S. Jalalzadeh, S. M. M. Rasouli and P. V. Moniz, Phys. Rev. D 90 (2014) 023541] up to a conformal scalar field content [T. Rostami, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 92 (2015) 023526, arXiv:gr-qc/1507.04212]. We envisage that we could extend this framework towards a class of shape invariant potentials, which could include well known analytically solvable cosmological cases. Provided, we identify integrability in terms of the shape invariance conditions, we could eventually consider to import features of supersymmetric quantum mechanics towards quantum cosmology [P. V. Moniz, Quantum Cosmology-the Supersymmetric Perspective-Vol. 1: Fundamentals, Lecture Notes in Physics, Vol. 803 (Springer-Verlag, Berlin, 2010), P. V. Moniz, Quantum Cosmology-the Supersymmetric Perspective-Vol. 2: Advanced Topics, Lecture Notes in Physics, Vol. 804 (Springer, New York, 2010)], which we will also discuss in this review.

Another point to emphasize is that by means of a hidden symmetry and then an algebra of Dirac observables, boundary conditions are extracted (and not ad hoc formulated) within a framework intrinsic to each model dynamics. Therefore, meeting DeWitt’s conjecture [B. S. DeWitt, Phys. Rev. 160 (1967) 1113] that “the constraints are everything” and nothing else but the constraints should be needed.

We have updated our analysis of the 9-year WMAP data using the collection of polarization maps looking for the presence of additional evidence for a finite ‘cosmic ray (CR) foreground’ for the cosmic microwave background (CMB). We have given special attention to high Galactic latitudes, where the recent BICEP2 findings were reported although very recent Planck data claims that dust is prevalent, thus nullifying the BICEP2 results. The method of examining the correlation with the observed gamma ray flux proposed in our earlier papers and applied to the polarization data shows that the foreground related to CRs is still observed even at high Galactic latitudes and conclusions about gravitational waves are not yet secure. Theory has it that there is important information about inflationary gravitational waves in the fine structure of the CMB polarization properties (polarization vector and angle) and it is necessary to examine further the conclusions that can be gained from studies of the CMB maps, in view of the disturbing foreground effects.

We find a class of charged black hole solutions in third-order Lovelock Gravity. To obtain this class of solutions, we are not confined to the usual assumption of maximal symmetry on the horizon and will consider the solution whose boundary is Einstein space with supplementary conditions on its Weyl tensor. The Weyl tensor of such exotic horizons exposes two chargelike parameter to the solution. These parameters in addition with the electric charge, cause different features in comparison with the charged solution with constant-curvature horizon. For this class of asymptotically (A)dS solutions, the electric charge dominates the behavior of the metric as $r$ goes to zero, and thus the central singularity is always timelike. We also compute the thermodynamic quantities for these solutions and will show that the first law of thermodynamics is satisfied. We also show that the extreme black holes with nonconstant-curvature horizons whose Ricci scalar are zero or a positive constant could exist depending on the value of the electric charge and chargelike parameters. Finally, we investigate the stability of the black holes by analyzing the behavior of free energy and heat capacity specially in the limits of small and large horizon radius. We will show that in contrast with charged solution with constant-curvature horizon, a phase transition occurs between very small and small black holes from a stable phase to an unstable one, while the large black holes show stability to both perturbative and nonperturbative fluctuations.

We analyze the properties of a generic cosmological fluid described by the van der Waals equation-of-state. Exact solutions for the energy-density evolution are found as implicit functions of the scale factor for a flat Friedmann–Robertson–Walker (FRW) spacetime. The possible values of the free parameter in the van der Waals equation are selected a posteriori, in accordance with asymptotic behaviors that are physically relevant. The stability of the model against small perturbations is studied through the hydrodynamic perturbations of the fluid for the relevant cases. It is found that a van der Waals fluid seems appropriate to describe noneternal inflationary scenarios.

In this paper, we have considered a spatially flat FRW universe filled with pressureless matter and dark energy (DE). We have considered a phenomenological parametrization of the deceleration parameter $q(z)$ and from this, we have reconstructed the equation-of-state (EoS) for DE ${\omega }_{\varphi }(z)$. This divergence-free parametrization of the deceleration parameter is inspired from one of the most popular parametrization of the DE EoS given by Barboza and Alcaniz [see E. M. Barboza and J. S. Alcaniz, Phys. Lett. B 666 (2008) 415]. Using the combination of datasets (Type Ia Supernova (SN Ia) + Hubble + baryonic acoustic oscillations/cosmic microwave background (BAO/CMB)), we have constrained the transition redshift $z_t$ (at which the universe switches from a decelerating to an accelerating phase) and have found the best fit value of $z_t$. We have also compared the reconstructed results of $q(z)$ and ${\omega }_{\varphi }(z)$ and have found that the results are compatible with a $\mathrm{\Lambda }$CDM universe if we consider SN Ia + Hubble data, but inclusion of BAO/CMB data makes $q(z)$ and ${\omega }_{\varphi }(z)$ incompatible with $\mathrm{\Lambda }$CDM model. The potential term for the present toy model is found to be functionally similar to a Higgs potential.

In this paper, we continue the study of the physical consequences of our modified black hole entropy formula in expanding spacetimes. In particular, we apply the new formula to apparent horizons of Friedmann expanding universes with zero, negative and positive spatial curvature. As a first result, we found that apart from the static Einstein solution, the only Friedmann spacetimes with constant (zero) internal energy are the ones with zero spatial curvature. This happens because, in the computation of the internal energy $U$, the contribution due to the nonvanishing Hubble flow must be added to the usual Misner–Sharp energy giving, for zero curvature spacetimes, a zero value for $U$. This fact does not hold when curvature is present. After analyzing the free energy $F$, we obtain the correct result that $F$ is stationary only for physical systems in isothermal equilibrium, i.e. a de Sitter expanding universe. This result permits us to trace back a physically reasonable hypothesis concerning the origin of the early and late times de Sitter phase of our universe. Finally, we deduce an interesting temperature–length inequality similar to the time–energy uncertainty of ordinary quantum mechanics but with temperature instead of time coordinate. Remarkably, this relation is independent of the gravitational constant $G$ and can thus be explored also in nongravitational contexts.

We consider the motion of a test particle orbiting around Reissner–Nordström (RN) black hole spacetime. The complete set of equations for radial motion and effective potential is derived. We also derive the radius of the different stable circular orbits of this particle corresponding to different label indexes like the Bohr atomic model. We also quantized the energy of this particle from the quantization of angular momentum and calculated the Bekenstein–Hawking entropy of RN black hole. We also investigate the change of entropy between two nearby states approaches to zero for large quantum numbers.

We study the impact of 1-loop radiative corrections in a nonsupersymmetric model of hybrid inflation (HI) with chaotic (polynomial-like) potential, $V_0+{\lambda }_p{\varphi }^p$. These corrections can arise from the possible couplings of inflaton with other fields which can play an active role in the reheating process. The tree-level predictions of these models are shown to lie outside of the Planck’s latest bounds on the scalar spectral index $n_s$ and the tensor to scalar ratio $r$. However, the radiatively corrected version of these models, $V_0+{\lambda }_p{\varphi }^p+A{\varphi }^{4}ln\varphi$, is fully consistent with the Planck’s data. More specifically, fermionic radiative correction ($A<0$) reduces the tensor to scalar ratio significantly and a red-tilted spectral index $n_s<1$, consistent with Planck’s data, is obtained even for sub-Planckian field-values.

Using a framework based on the $1+3$ formalism, we carry out a study on axially and reflection symmetric dissipative fluids, in the quasi-static regime. We first derive a set of invariantly defined “velocities”, which allow for an inambiguous definition of the quasi-static approximation. Next, we rewrite all the relevant equations in this approximation and extract all the possible, physically relevant, consequences ensuing the adoption of such an approximation. In particular, we show how the vorticity, the shear and the dissipative flux, may lead to situations where different kind of “velocities” change their sign within the fluid distribution with respect to their sign on the boundary surface. It is shown that states of gravitational radiation are not a priori incompatible with the quasi-static regime. However, any such state must last for an infinite period of time, thereby diminishing its physical relevance.

In this paper, we investigate the effect of anisotropic stresses (radial and tangential pressures being unequal) for a collapsing fluid sphere dissipating energy in the form of radial flux. The collapse starts from an initial static sphere described by the Bowers and Liang solution and proceeds until the time of formation of the horizon. We find that the surface redshift increases as the stellar fluid moves away from isotropy. We explicitly show that the formation of the horizon is delayed in the presence of anisotropy. The evolution of the temperature profiles is investigated by employing a causal heat transport equation of the Maxwell–Cattaneo form. Both the Eckart and causal temperatures are enhanced by anisotropy at each interior point of the stellar configuration.

We examine the evolution of universe in $f(R,\tau )$ gravity where $R$ is the Ricci curvature and $\tau$ is the trace of energy–momentum tensor. We focus on the specific form $f(R,\tau )=R+f(\tau )$ and explicitly find out the relation between $f(\tau )$ and state of equation $w$ by adiabatic condition. All possible modes of evolution of the scale factor for the five kinds of state of equation, $w=\pm 1,\pm \frac{1}{3},0$ are exhibited. We simulate numerically the plots of redshift versus distance modulus for three interesting modes and then obtain the good fitting curve compared with the astronomical observation data.

The Hertz potential is a powerful tool for the source-free electrodynamics. Especially for the algebraically special spacetime background, the Hertz potential formalism simplifies the Maxwell equations quite much. In astrophysics, strong electric–magnetic field is very common. Force-free electrodynamics is a good approximation for strong enough electric–magnetic field compared to the inertial energy of the involved plasma. For example, the force-free model has been extensively used to describe the magnetosphere of stars in the universe. In this paper, we extend the Hertz potential formalism to the force-free electrodynamics. The Hertz potential formalism simplifies the force-free dynamical equations as much as that in the source-free case. As an application, we use the Hertz potential formalism to the Schwarzschild background. And the Brennan–Gralla–Jacobson solutions are recovered straightforwardly.