General Relativity and Quantum Cosmology (gr-qc)

Abstract: We investigate entanglement of local spatial modes defined by a quantum field in a de Sitter universe. The introduced modes show dis-entanglement behavior when the separation between two regions where local modes are assigned becomes larger than the cosmological horizon. To understand the emergence of separability between these local modes, we apply the monogamy inequality proposed by S. Camalet. We embed the focusing bipartite mode defined by the quantum field in a pure four-mode Gaussian state, and identify its partner modes. Then applying a Gaussian version of the monogamy relation, we show that the external entanglement between the bipartite mode and its partner modes constrains the entanglement of the bipartite mode. Thus the emergence of separability of local modes in the de Sitter universe can be understood from the perspective of entanglement monogamy.

Abstract: The luminosity distance is a key observable of gravitational-wave observations. We demonstrate how one can correctly retrieve the luminosity distance of compact binary coalescences if the gravitational-wave signal is strongly lensed. We perform a proof-of-concept parameter estimation for the luminosity distance supposing (i) strong lensing produces two lensed gravitational-wave signals, (ii) the advanced LIGO-Virgo network detects both lensed signals as independent events, and (iii) the two events are identified as strongly lensed signals originated from a single compact binary coalescence. Focusing on the maximum magnification allowed in the given lensing scenario, we find that the strong lensing can improve the precision of the distance estimation by up to a factor of two compared to that can be expected for the signal experiencing no lensing. Our results imply that strong lensing of gravitational waves can be helpful for better constraining the distance to the source, and furthermore, the Hubble constant.

Abstract: In my thesis, I present one particular example of the formalism capable of describing the propagation of a family of light rays in a curved spacetime. It is based on the resolvent operator of the geodesic deviation equation for null geodesics which is known as the bilocal geodesic operator (BGO) formalism. The BGO formalism generalizes the standard treatment of light ray bundles by allowing observations extended in time or performed by a family of neighbouring observers. Furthermore, it provides a more unified picture of relativistic geometrical optics and imposes a number of consistency requirements between the optical observables. The thesis begins with a brief introduction of the transfer matrix and its relativistic versions known as the Jacobi propagators and the bilocal geodesic operators. Then the basics of differential geometry are reviewed, with an emphasis on the geometry of the tangent bundle and the geodesic flow, which later provide the foundation for the BGO formalism. The mathematical introduction is then followed by two articles about the applications of the BGO formalism in the studies of optical distance measures and the conclusion.

Abstract: This work explores various manifestations of bumblebee gravity within the metric--affine formalism. We investigate the impact of Lorentz violation parameter, denoted as $X$, on the modification of the \textit{Hawking} temperature. Our calculations reveal that as $X$ increases, the values of the \textit{Hawking} temperature attenuate. To examine the behavior of massless scalar perturbations, specifically the \textit{quasinormal} modes, we employ the WKB method. The transmission and reflection coefficients are determined through our calculations. The outcomes indicate that a stronger Lorentz--violating parameter results in slower damping oscillations of gravitational waves. To comprehend the influence of the \textit{quasinormal} spectrum on time--dependent scattering phenomena, we present a detailed analysis of scalar perturbations in the time--domain solution. Additionally, we conduct an investigation on shadows, revealing that larger values of $X$ correspond to larger shadow radii. Lastly, we explore the concept of time delay within this framework.

Abstract: Candidate microstates of a spherically symmetric geometry are constructed in the group field theory formalism for quantum gravity, for models including both quantum geometric and scalar matter degrees of freedom. The latter are used as a material reference frame to define the spacetime localization of the various elements of quantum geometry. By computing quantum geometric observables, we then match the quantum states with a spherically symmetric classical geometry, written in a suitable matter reference frame.

Abstract: The present work deals with the classical and quantum aspects of the Raychaudhuri equation in the framework of f(T)-gravity theory. In the background of homogeneous and isotropic Friedmann Lemaitre Robertson Walker space time, the Raychaudhuri equation has been formulated and used to examine the focusing theorem and convergence condition for different choices of f(T). Finally in quantum cosmology, the wave function of the universe has been shown to be the energy eigen function of the time independent Schrodinger equation of a particle. Also probability measure on the mini-super space has been examined at zero volume for singularity analysis in the quantum regime. Lastly the Bohmian trajectory for the present quantum system has been explicitly determined for some particular choices.

Abstract: Recent developments in deep learning techniques have offered an alternative and complementary approach to traditional matched filtering methods for the identification of gravitational wave (GW) signals. The rapid and accurate identification of GW signals is crucial for the progress of GW physics and multi-messenger astronomy, particularly in light of the upcoming fourth and fifth observing runs of LIGO-Virgo-KAGRA. In this work, we use the 2D U-Net algorithm to identify the time-frequency domain GW signals from stellar-mass binary black hole (BBH) mergers. We simulate BBH mergers with component masses from 5 to 80 $M_{\odot}$ and account for the LIGO detector noise. We find that the GW events in the first and second observation runs could all be clearly and rapidly identified. For the third observation run, about $80\%$ GW events could be identified and GW190814 is inferred to be a BBH merger event. Moreover, since the U-Net algorithm has advantages in image processing, the time-frequency domain signals obtained through U-Net can preliminarily determine the masses of GW sources, which could help provide the mass priors for future parameter inferences. We conclude that the U-Net algorithm could rapidly identify the time-frequency domain GW signals from BBH mergers and provide great help for future parameter inferences.

Abstract: In a talk given in 2013, S. Hawking conjectured that the event horizon of black holes does not exist and suggested redefining black holes as bound states of the gravitational field. Inspired by this idea, we investigated the coupling of the Bardeen action and a complex scalar field model. Numerically, we obtained a class of boson stars solutions with the magnetic monopole charge $q$. When the constant $q$ exceeds a certain threshold, we observed that as the frequency approaches zero, a critical position $r_c$ emerges where the scalar field concentrates within its interior. Outside this critical position, these boson star solutions tend to infinitely approach what is known as an extreme black hole. However, there is no event horizon present. While our results are model-dependent and their generality remains uncertain, they align well with Hawking's conjecture that real, regular black holes do not have an event horizon and provided valuable insights into the understanding and development of concepts such as fuzzballs, firewalls and black hole soft hairs.

Abstract: This work explores the dynamical stability of cosmological models where dark matter and dark energy can non-minimally couple to spacetime (scalar) curvature. Two different scenarios are presented here. In the initial case, only dark matter sector is coupled to curvature in the presence of a quintessence scalar field. In the second case both dark matter and the quintessence field are coupled to curvature. It is shown that one can get an accelerating expansion phase of the universe in both the cases. The nature of the fixed points show that there can be stable or unstable phases where the curvature coupling vanishes and dark energy and dark matter evolve independently. On the other hand there can be stable accelerating expansion phases where both the components are coupled to curvature.

Abstract: The conformal correspondence between FLRW universes in the Einstein and Jordan frames allows for an expansion-collapse duality -- an always expanding Einstein frame universe can have a dual Jordan frame description that is contracting forever. The scenario eventually runs into an apparent paradox. When a collapsing universe approaches singularity, the classical description of the spacetime becomes inadequate. The contracting Jordan frame universe is expected to develop quantum characteristics when its scale factor becomes sufficiently small. However, at the same time, the corresponding Einstein frame universe is expected to behave classically, due to the arbitrarily large size it has grown to. In this case, the conformal map appears to be providing a duality between a quantum effect-dominated universe and a universe behaving classically. We investigate the status of the conformal map at the quantum level in such a scenario, focusing on addressing this paradox. The Einstein and Jordan frame universes are quantized individually using the Wheeler-DeWitt prescription. We show that the classical conformal map holds true at the quantum level when compared through the expectation values of the scale factor operators in the two frames. The relative quantum fluctuation in the scale factor is found to be conformally invariant, and it increases in both the past and future directions according to the internal clock. Expectedly, the quantum fluctuations in the collapsing Jordan frame keep on increasing as it shrinks towards singularity. More surprisingly, the quantum fluctuations in the expanding Einstein frame keep on increasing as well, even as its classical scale factor becomes larger. Despite having drastically different cosmological evolutions, the rise in quantum characteristics in a collapsing frame implies the same in its expanding counterpart, thereby resolving the apparent paradox.

Abstract: We investigate the inflation and reheating phenomenology in scalar-Einstein-Gauss-Bonnet theory of gravity where a scalar field non-minimally couples with the Gauss-Bonnet (GB) curvature term. Regarding the inflationary phenomenology, we find -- (1) the inflation starts with a quasi de-Sitter phase and has an exit at a finite e-fold, (2) the scalar and tensor perturbations prove to be ghost free and do not suffer from gradient instability, (3) the curvature perturbation amplitude as well as its tilt and the tensor-to-scalar ratio turn out to be simultaneously compatible with the recent Planck data for suitable values of the parameters. After the inflation ends, the scalar field starts to decay to radiation with a constant decay width. For our considered scalar potential and the GB coupling function, the model results to an analytic power law solution of the Hubble parameter and a logarithmic solution of the scalar field during the reheating era, where the exponent of the Hubble parameter determines the effective EoS parameter ($w_\mathrm{eff}$) during the same. The stability of such reheating dynamics is examined by dynamical analysis which ensures that $w_\mathrm{eff}$ can go beyond unity and reach up-to the maximum value of $\mathrm{max}(w_\mathrm{eff}) = 1.56$. The scenario with $w_\mathrm{eff} > 1$ proves to be purely due to the presence of the GB coupling function, which in turn may have important consequences on enhancing the primordial gravitational waves' amplitude observed today. The inflationary e-fold number gets further constrained by the input of the reheating stage. We finally construct the complete forms of scalar potential ($V(\phi)$) and the GB coupling ($\xi(\phi)$) function that smoothly transits from inflation to reheating, and numerically solve the Hubble parameter and the scalar field for such complete forms of $V(\phi)$ and $\xi(\phi)$.

Abstract: In this paper we have constructed the unconstrained action for the perturbations above Bianchi I type background in the most general scalar-tensor theory of gravity, the Horndeski theory. The result could be used now in the context of anisotropic early Universe models, no-go theorems and general stability and in anisotropic probes of current cosmological perturbations.