General Relativity and Quantum Cosmology (gr-qc)

Abstract: The growing cosmological interest of different entropy functions (like the Tsallis entropy, the R\'{e}nyi entropy, the Barrow entropy, the Sharma-Mittal entropy, the Kaniadakis entropy and the Loop Quantum gravity entropy) naturally raises an important question: "Does there exist a generalized entropy that can bring all the known entropies proposed so far within a single umbrella?" In spirit of this, recently a four parameter generalized entropy has been formulated that reduces to different known entropies for suitable limits of the parameters. Based on such four parameter generalized entropy (symbolized by $S_\mathrm{g}$), in the present paper, we examine the universe's evolution during its early phase, particularly from inflation to reheating, in the context of entropic cosmology where the entropic energy density acts as the inflaton. It turns out that the entropic energy successfully drives an early inflationary phase with a graceful exit, and moreover, the theoretical expectations of the observable indices get consistent with the recent Planck data for suitable ranges of the entropic parameters. After the inflation ends, the universe enters to a reheating stage when the entropic energy decays to relativistic particles with a certain decay rate. Actually the presence of the entropic parameters in the $S_\mathrm{g}$ ensures a continuous evolution of the Hubble parameter from a quasi de-Sitter phase during the inflation to a power law phase during the reheating stage dominated by a constant EoS parameter. Consequently we investigate the reheating phenomenology, and scan the entropic parameters from both the inflation and reheating requirements. We further address the possibility of instantaneous reheating in the present context of generalized entropy.

Abstract: Effective one body numerical relativity waveform models for spin aligned binary black holes (SEOBNR) are based on the effective one body theoretical framework and numerical relativity simulation results. SEOBNR models have evolved through version 1 to version 4. We recently extended SEOBNRv1 model to SEOBNRE (Effective One Body Numerical Relativity waveform models for Spin aligned binary black holes along Eccentric orbit) model which is also valid for spin aligned binary black hole coalescence along eccentric orbit. In this paper we update our previous SEOBNRE model to make it consistent to SEOBNRv4 which is the most widely used SEOBNR waveform model. This upgraded SEOBNRE model improves accuracy compared to previous SEOBNRE model, especially for highly spinning black holes. For spin aligned binary black holes with mass ratio $1\leq q\lesssim10$, dimensionless spin $-0.9\lesssim\chi\lesssim0.995$ and orbital eccentricity $0\leq e_0\lesssim0.6$ at reference frequency $Mf_0=0.002$ ($M$ is the total mass of the binary black hole, $f_0\approx 40\frac{10{\rm M}_\odot}{M}$Hz), the upgraded SEOBNRE model can always fit numerical relativity waveform better than 98.2\%. For most cases the fitting factor can even be better than 99\%.

Abstract: The equations for quintessential $\alpha$-attractor inflation with a single scalar field, radiation and matter in a spatially flat FLRW spacetime are recast into a regular dynamical system on a compact state space. This enables a complete description of the solution space of these models. The inflationary attractor solution is shown to correspond to the unstable center manifold of a de Sitter fixed point, and we describe connections between slow-roll and dynamical systems approximations for this solution, including Pad\'e approximants. We also introduce a new method for systematically obtaining initial data for quintessence evolution by using dynamical systems properties; in particular, this method exploits that there exists a radiation dominated line of fixed points with an unstable quintessence attractor submanifold, which plays a role that is reminiscent of that of the inflationary attractor solution for inflation.

Abstract: The asymptotic behaviour of massless spin-0 fields close to spatial and null infinity in Minkowski spacetime is studied by means of Friedrich's cylinder at spatial infinity. The results are applied to a system of equations called the good-bad-ugly which serves as a model for the Einstein field equations in generalised harmonic gauge. The relation between the logarithmic terms (polyhomogeneity) appearing in the solution obtained using conformal methods and those obtained by means of a heuristic method based on H\"ormander's asymptotic system is discussed. This review article is based on Class. Quantum Grav. 40 055002 and arXiv:2304.11950.

Abstract: In this paper, we present a rotating de Rham-Gabadadze-Tolley black hole with a positive cosmological constant in massive gravity, achieved by applying a modified Newman-Janis algorithm. The black hole exhibits stable orbits of constant radii, prompting a numerical study on the behavior of the solutions to a nonic equation governing the radii of planar orbits around the black hole. Additionally, we investigate the stability of orbits near the event horizon and provide a comprehensive analytical examination of the solutions to the angular equations of motion. This is followed by simulating some spherical particle orbits around the black hole.

Abstract: We investigate within the Darmois-Israel thin shell formalism the match of neutral and asymptotically flat, slowly rotating spacetimes (up to the second order in the rotation parameter) when their boundaries are dynamic. It has several important applications in general relativistic systems, such as black holes and neutron stars, which we exemplify. We mostly focus on stability aspects of slowly rotating thin shells in equilibrium and surface degrees of freedom on the hypersurfaces splitting the matched slowly rotating spacetimes, e.g., surface energy density and surface tension. We show that the stability upon perturbations in the spherically symmetric case automatically implies stability in the slow rotation case. In addition, we show that when matching slowly rotating Kerr spacetimes through thin shells in equilibrium, surface degrees of freedom can decrease compared to their Schwarzschild counterparts, meaning that energy conditions could be weakened. Frame-dragging aspects of the match of slowly rotating spacetimes are also briefly discussed.

Abstract: We study the convergence of the path integral for General Relativity with matter on a picewise linear (PL) spacetime that corresponds to a triangulation of a smooth manifold by using a path-integral measure that renders the pure gravity path integral finite. This measure depends on a parameter p, and in the case when the matter content is just scalar fields, we show that the path integral is absolutely convergent for p > 0,5 and not more than 2 scalar fields. In the case of Yang-Mills fields, we show that the path integral is absolutely convergent for the U(1) group and p > 0,5. In the case of Dirac fermions, we show that the path integral is absolutely convergent for any number of fermions and a sufficiently large p. When the matter content is given by scalars, Yang-Mills fields and fermions, as in the case of the Standard Model, we show that the path integral is absolutely convergent for p > 46,5. Hence one can construct a finite quantum gravity theory on a PL spacetime such that the classical limit is General Relativity coupled to the Standard Model.

Abstract: Loops of inflationary gravitons are known to induce large temporal and spatial logarithms which can cause perturbation theory to break down. Nonlinear sigma models possess the same kind of derivative interactions and induce the same sorts of large logarithms, without the complicated index structure and potential gauge problem. Previous studies have examined models with zero field space curvature which can be reduced to free field theories by local, invertible field redefinitions. Here we study a model which cannot be so reduced and still shows the same sorts of large logarithms. We compute the evolution of the background at 1-loop and 2-loop orders, and we find the 1-loop $\beta$ and $\gamma$ functions.

Abstract: We discuss the problem of the quantization and dynamic evolution of a scalar free field in the interior of a Schwarzschild black hole. A unitary approach to the dynamics of the quantized field is proposed: a time-dependent Hamiltonian governing the Heisenberg equations is derived. It is found that the system is represented by a set of harmonic oscillators coupled via terms corresponding to the creation and annihilation of pairs of particles and that the symmetry properties of the spacetime, homogeneity and isotropy are obeyed by the coupling terms in the Hamiltonian. It is shown that Heisenberg equations for annihilation and creation operators are transformed into ordinary differential equations for appropriate Bogolyubov coefficients. Such a formulation leads to a general question concerning the possibility of gravitationally driven instability, that is however excluded in this case.

Abstract: Large frame Ring laser gyroscopes, based on the Sagnac effect, are top sensitivity instrumentation to measure angular velocity with respect to the fixed stars. GINGER (Gyroscopes IN GEneral Relativity) project foresees the construction of an array of three large dimension ring laser gyroscopes, rigidly connected to the Earth. GINGER has the potentiality to measure general relativity effects and Lorentz Violation in the gravity sector, once a sensitivity of $10^{-9}$, or better, of the Earth rotation rate is obtained. Being attached to the Earth crust, the array will also provide useful data for geophysical investigation. For this purpose, it is at present under construction as part of the multi-components observatory called Underground Geophysics at Gran Sasso (UGSS). Sensitivity is the key point to determine the relevance of this instrument for fundamental science. The most recent progress in the sensitivity measurement, obtained on a ring laser prototype called GINGERINO, indicates that GINGER should reach the level of 1 part in $10^{11}$ of the Earth rotation rate.

Abstract: We study the impact of out-of-equilibrium, dissipative effects on the dynamics of inspiraling neutron stars. We find that modeling dissipative processes (such as those from the stars internal effective fluid viscosity) requires that one introduce a new tidal deformability parameter--the dissipative tidal deformability--which modifies the phase of gravitational waves emitted during the inspiral phase of a neutron star binary. We show that the dissipative tidal deformability corrects the gravitational-wave phase at 4 post-Newtonian order for quasi-circular binaries. This correction receives a large finite-size enhancement by the stellar compactness, analogous to the case of the tidal deformability. Moreover, the correction is not degenerate with the time of coalescence, which also enters at 4PN order, because it contains a logarithmic frequency-dependent contribution. Using a simple Fisher analysis, we show that physically allowed values for the dissipative tidal deformability may be constrained by measurements of the phase of emitted gravitational waves to roughly the same extent as the (electric-type, quadrupolar) tidal deformability. Finally, we show that there are no out-of-equilibrium, dissipative corrections to the tidal deformability itself. We conclude that there are at least two relevant tidal deformability parameters that can be constrained with gravitational-wave phase measurements during the late inspiral of a neutron star binary: one which characterizes the adiabatic tidal response of the star, and another which characterizes the leading-order out-of-equilibrium, dissipative tidal response. These findings open a window to probe dissipative processes in the interior of neutron stars with gravitational waves.