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Hawking's singularity theorem says that cosmological solutions arising from initial data with positive mean curvature have a past singularity. However, the nature of the singularity remains unclear. We therefore ask: If the initial…
We present a review of cosmological solutions in non-linear massive gravity, focusing on the stability of perturbations. Although homogeneous and isotropic solutions have been found, these are now known to suffer from either Higuchi ghost…
The Born-Infeld determinantal gravity has been recently proposed as a way to smooth the Big Bang singularity. This theory is formulated on the Weitzenbock space-time and the teleparallel representation is used instead of the standard…
We show that simple scalar field models can give rise to curvature singularities in the effective Friedmann dynamics of Loop Quantum Cosmology (LQC). We find singular solutions for spatially flat Friedmann-Robertson-Walker cosmologies with…
We consider scalar perturbations in the time-dependent Ho\u{r}ava-Witten Model in order to probe its stability. We show that during the non-singular epoque the model evolves without instabilities until it encounters the curvature…
In this paper we provide approximate analytical analysis of stability of nonsingular inflationary chaotic-type cosmological models. Initial conditions for nonsingular solutions at the bounce correspond to dominance of potential part of the…
A variety of conditions is considered under which the cosmic dark fluid may be able to develop a future Big Rip or Little Rip singularity. Both one-component and two-component models are considered. In the last-mentioned case we present a…
Motivated by condensed matter physical systems, in which a finite-time singularity indicates that the topology of the system changes, we critically examine the possibility of the Universe's topology change at a finite-time cosmological…
We review recent work on the existence and nature of cosmological singularities that can be formed during the evolution of generic as well as specific cosmological spacetimes in general relativity. We first discuss necessary and sufficient…
The properties of future singularities are investigated in the universe dominated by dark energy including the phantom-type fluid. We classify the finite-time singularities into four classes and explicitly present the models which give rise…
This article gives a concise overview of the development and current status of studies on healthy models of the early Universe without an initial singularity, namely the cosmological bounce and Genesis scenarios, constructed within a broad…
The big bounce singularity of a simple 5D cosmological model is studied. Contrary to the standard big bang space-time singularity, this big bounce singularity is found to be an event horizon at which the scale factor and the mass density of…
The stability of cosmological solutions in the recently suggested specific mechanism of dynamical compensation of vacuum energy is studied. It is found that the solutions in the original version lead to cosmological singularity which could…
In this work we analyze the possibility of sudden cosmological singularities, also known as type-II singularities, in the background of a Friedmann-Lema\^itre-Robertson-Walker (FLRW) geometry in an extension of General Relativity (GR) known…
The relation between the long wavelength limit of solutions to the cosmological perturbation equations and the perturbations of solutions to the exactly homogeneous background equations is investigated for scalar perturbations on spatially…
We study the properties of cosmological density perturbations in a multi-component system consisting of a scalar field and a perfect fluid. We discuss the number of degrees of freedom completely describing the system, introduce a full set…
We show that the problem of stabilization of extra dimensions in Kaluza-Klein type cosmology may be solved in a theory of gravity involving high-order curvature invariants. The method suggested (employing a slow-change approximation) can…
We prove the nonlinear stability, in the contracting direction, of the entire subcritical family of Kasner-scalar field solutions to the Einstein-scalar field equations in four spacetime dimensions. Our proof relies on a zero-shift,…
We study a model of a scalar field minimally coupled to gravity, with a specific potential energy for the scalar field, and include curvature and radiation as two additional parameters. Our goal is to obtain analytically the complete set of…
In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…