General Relativity And Quantum Cosmology

We study the distribution and generation of quantum coherence for two-mode and multi-mode Gaussian states in de Sitter space. It is found that the quantum coherence is redistributed among the mode in different open charts under the curvature effect of de Sitter space. In particular, the Gaussian coherence for the initially correlated state is found to survive in the limit of infinite curvature, while quantum entanglement vanishing in this limit. Unlike entanglement and steering, the coherence of a massive scalar field is more robust than a massless field under the influence of curvature of de Sitter space. In addition, it is shown that the curvature generates two-mode Gaussian state and three-mode Gaussian state quantum coherence among the open charts, even though the observers are localized in causally disconnected regions. It is worth noting that the gravity-generated three-mode coherence is extremely sensitive to the curvature effect for the conformal and massless scalar fields, which may be in principle employed to design an effective detector for the space curvature.

In this paper the Feynman Green function for Maxwell's theory in curved space-time is studied by using the Fock-Schwinger-DeWitt asymptotic expansion; the point-splitting method is then applied, since it is a valuable tool for regularizing divergent observables. Among these, the stress-energy tensor is expressed in terms of second covariant derivatives of the Hadamard Green function, which is also closely linked to the effective action; therefore one obtains a series expansion for the stress-energy tensor. Its divergent part can be isolated, and a concise formula is here obtained: by dimensional analysis and combinatorics, there are two kinds of terms: quadratic in curvature tensors (Riemann, Ricci tensors and scalar curvature) and linear in their second covariant derivatives. This formula holds for every space-time metric; it is made even more explicit in the physically relevant particular cases of Ricci-flat and maximally symmetric spaces, and fully evaluated for some examples of physical interest: Kerr and Schwarzschild metrics and de Sitter space-time.

We investigate the interior of the Einstein-Gauss-Bonnet charged black-hole with scalar hair. We find a variety of dynamical epochs, with the particular important feature that the Cauchy horizon is not present. This makes the violation of the no-hair theorem a possible tool to understand how might the strong cosmic censorship conjecture work.

The dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein's equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities -- qua part of a physical law -- highlight some kind of a posteriori necessity in a Kripkean sense. The inquiry shows that general relativistic physics has an interesting bearing on the debate about the metaphysics of the laws of nature.

In this thesis, we attempt to gain a more complete insight into Double Layer Theories in Weyl Gravity. In order to do this, we first establish the premise of Weyls Theory, including its provenance, development and flaws. This is all discussed in the first five chapters of the thesis. After having established Weyls Infinitesimal geometry and his gauged (scalar-tensor) gravity theory, we move onto the topic at hand, namely, Double Layers. We define the action to be used and describe the volume of integration (especially the Singular Hyper Surface) across which the action principle is setup. We define our gauss Normal Coordinate system and the scheme which we follow when we undertake our calculation. The following sections detail the variation process, in a succinct manner, taking turn by turn, each of the four parameters of our Quadratic Lagrangian. In the last chapter, we conclude the thesis by gleaning out the meaning behind our newfound surface energy tensor terms and what they might imply physically, as well as drawing a clearer picture of contrast between General Relativity and Weyl gravity.

We consider reflection-asymmetric thin-shell wormholes within Palatini f(R) gravity using a matching procedure of two patches of electrovacuum space-times at a hypersurface (the shell) via suitable junction conditions. The conditions for having (linearly) stable wormholes supported by positive-energy matter sources are determined. We also identify some subsets of parameters able to locate the shell radius above the event horizon (when present) but below the photon sphere (on both sides). We illustrate with an specific example that such two photon spheres allow an observer on one of the sides of the wormhole to see another (circular) shadow in addition to the one generated by its own photon sphere, which is due to the photons passing above the maximum of the effective potential on its side and bouncing back across the throat due to a higher effective potential on the other side. We finally comment on the capability of these double shadows to seek for traces of new gravitational physics beyond that described by General Relativity.

The simple structure of doubly torqued vectors allows for a natural characterization of doubly twisted down to warped spacetimes, as well as Kundt spacetimes down to PP waves. For the first ones the vectors are timelike, for the others they are null. We also discuss some properties, and their connection to hypersurface orthogonal conformal Killing vectors, and null Killing vectors.

We solve for a system that emits acceleration radiation at two different temperatures. The equilibrium states occur asymptotically in Planck distributions and transition non-thermally. The model is simple enough to obtain a global solution for the radiation spectrum analytically. We present it as a potentially useful model for investigation of non-thermal vacuum acceleration radiation in the presence of final(initial) asymptotic thermodynamic horizon(less) states in equilibrium.

Our first goal in this work is to study general and model-independent properties of cyclic cosmologies. The large number of studies of bouncing cosmologies and different cyclic scenarios published recently calls for a proper understanding of the universal properties of cyclic models. We thus first review and further elaborate the common physical and geometrical properties of various classes of cyclic models and then discuss how cyclic Universe can be treated as a dynamic system. We then discuss how two theorems from dynamic systems analysis can be used to ensure the existence of cyclic cosmological solutions under certain conditions on the field equations. After this we proceed towards our second goal which is the application of the obtained results to different frameworks of modified gravity theories: f(R) gravity, dynamic dark energy and f(T) gravity. We discuss the general requirements for the existence of cyclic solutions in these theories and also obtain various examples of cyclic cosmologies, while discussing their basic properties.

In this article, we summarize two agnostic approaches in the framework of spatially curved Friedmann-Robertson-Walker (FRW) cosmologies discussed in detail in (Kerachian et al., 2020, 2019). The first case concerns the dynamics of a fluid with an unspecified barotropic equation of state (EoS), for which the only assumption made is the non-negativity of the fluid's energy density. The second case concerns the dynamics of a non-minimally coupled real scalar field with unspecified positive potential. For each of these models, we define a new set of dimensionless variables and a new evolution parameter. In the framework of these agnostic setups, we are able to identify several general features, like symmetries, invariant subsets and critical points, and provide their cosmological interpretation.