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We examine the implementation of Buchert's and Green & Wald's averaging formalisms in exact spherically symmetric and plane symmetric dust-filled cosmological models. We find that, given a cosmological space-time, Buchert's averaging scheme…
Backreaction effects of the large scale structure on the background dynamics have been claimed to lead to a renormalization of the background dynamics that may account for the late time acceleration of the cosmic expansion. This article…
The general relativistic non--linear dynamics of a self--gravitating collisionless fluid with vanishing vorticity is studied in synchronous and comoving -- i.e. {\em Lagrangian} -- coordinates. Writing the equations in terms of the metric…
The properties of universes are explored that are entirely in the interior of black holes in another universe, a `mother universe'. It is argued that these models offer a paradigm that may shed a new light on old cosmological problems. The…
Models of inhomogeneous universes constructed with exact solutions of Einstein's General Relativity have been proposed in the literature with the aim of reproducing the cosmological data without any need for a dark energy component. Besides…
We investigate the effects of the underlying quantum geometry in loop quantum cosmology on spacetime curvature invariants and the extendibility of geodesics in the Bianchi-I model for matter with a vanishing anisotropic stress. Using the…
Inhomogeneous cosmological models have had significant success in explaining cosmological observations without the need for dark energy. Generally, these models imply inhomogeneous matter distributions alter the observable relations that…
We attempt to study three significant tests of general relativity in higher dimensions both in commutative and non-commutative spaces. In the context of non-commutative geometry, we will consider a solution of the Einstein equation in…
In this thesis, we try to resolve the alleged problem of non-unitarity for various anisotropic cosmological models. Using Wheeler-DeWitt formulation, we quantized the anisotropic models with variable spatial curvature, namely Bianchi II and…
The inhomogeneous cosmological model with matter in the form self-acting scalar field and perfect fluid is considered. On the basis of exact solutions is considered the evolution of density distribution of a matter in space on a background…
Alternative gravitational theories described by Lagrangians depending on general functions of the Ricci scalar have been proven to give coherent theoretical models to describe the experimental evidence of the acceleration of universe at…
An expression for the average redshift drift in a statistically homogeneous and isotropic dust universe is given. The expression takes the same form as the expression for the redshift drift in FLRW models. It is used for a…
If one is willing to give up the cherished hypothesis of spatial isotropy, many interesting cosmological models can be developed beyond the simple anisotropically expanding scenarios. One interesting possibility is presented by shear-free…
We prove several inequalities between the curvature invariants, which impose constraints on curvature singularities. Some of the inequalities hold for a family of spacetimes which include static, Friedmann--Lema\^itre--Robertson--Walker,…
We establish purely geometric or metric-based criteria for the validity of the separate universe ansatz, under which the evolution of small-scale observables in a long-wavelength perturbation is indistinguishable from a separate…
We investigate effective equations governing the volume expansion of spatially averaged portions of inhomogeneous cosmologies in spacetimes filled with an arbitrary fluid. This work is a follow-up to previous studies focused on irrotational…
This paper investigates the influence of non-commutative geometry on various aspects of neutrino behavior in curved spacetime. Adopting a Schwarzschild-like black hole solution with Lorentzian mass deformation induced by non-commutativity,…
The scattering of a Gaussian wavepacket in armchair and zigzag graphene edges is theoretically investigated by numerically solving the time dependent Schr\"odinger equation for the tight-binding model Hamiltonian. Our theory allows to…
Time evolution of a black hole lattice universe is simulated. The vacuum Einstein equations in a cubic box with a black hole at the origin are numerically solved with periodic boundary conditions on all pairs of opposite faces. Defining…
Planck-scale quantum spacetime undergoes probabilistic local curvature fluctuations whose distributions cannot explicitly depend on position otherwise vacuum's small-scale quantum structure would fail to be statistically homogeneous. Since…