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FRW models of the universe have been studied in the cosmological theory based on Lyra's manifold. A new class of exact solutions has been obtained by considering a time dependent displacement field for variable deceleration parameter from…
The mechanism for the relaxation of the cosmological constant is studied and elaborated. In the model used for the analysis of the relaxation mechanism the universe contains two components: a cosmological constant of an arbitrary size and…
In the generalized matter-geometry coupling theory, we investigate the physical characteristics and causality of some new cosmological models for a flat, homogeneous, and isotropic spacetime filled with stiff, radiation, dust, and curvature…
We discuss some problems related to dimensional reductions of gravity theories to two-dimensional and one-dimensional dilaton gravity models. We first consider the most general cylindrical reductions of the four-dimensional gravity and…
We study the behavior of a general gravitational action, including quadratic terms in the curvature, supplemented by a compact scalar field in 4+1 dimensions. The generalized Einstein equation for this system admits solutions which are…
We investigate late time acceleration of the universe in higher dimensional cosmology. The content in the universe is assumed to exert pressure which is different in the normal and extra dimensions. Cosmologically viable solutions are found…
We explore the effects of background cosmology on large scale structures with non-spherical symmetry by using the concept of quasi-equilibrium which allows certain internal properties (e.g. angular velocity) of the bodies to change with…
The higher dimensional Quantum General Relativity of a Riemannian manifold being an embedded space in a space-time being a Lorentzian manifold is investigated. The model of quantum geometrodynamics, based on the Wheeler-DeWitt equation…
The exploration of teleparallel gravity has been done from a dynamical systems point of view in order to be tested against the cosmological evolution currently observed. So far, the proposed autonomous systems have been restrictive over a…
The three-body problem is a fundamental long-standing open problem, with applications in all branches of physics, including astrophysics, nuclear physics and particle physics. In general, conserved quantities allow to reduce the formulation…
The current expansion of the Universe has been observed to be accelerating, and the widely accepted spatially-flat concordance model of general relativistic cosmology attributes this phenomenon to a constant dark energy, a cosmological…
The field equations of modified gravity theories, when considering a homogeneous and isotropic cosmological model, always become autonomous differential equations. This relies on the fact that in such models all variables only depend on…
In this paper the observational consequence of the cosmological models and the expression for the neoclassical tests, luminosity distance, angular diameter distance and look back time are analyzed in the framework of Lyra geometry. It is…
Some aspects of two General Relativistic cosmological solutions, an exact $\Lambda$CDM-like cosmological solution $j=1$ ($j$ is cosmographic jerk parameter), and a specifically designed toy cosmological solution $j=1+3\varepsilon(q-1/2)$…
A number of dynamical system formulations have been proposed over the last few years to analyse cosmological solutions in $f(R)$ gravity. The aim of this article is to provide a brief introduction to the different approaches, presenting…
We describe a class of integrable models of 1+1 and 1-dimensional dilaton gravity coupled to scalar fields. The models can be derived from high dimensional supergravity theories by dimensional reductions. The equations of motion of these…
We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for…
In this work we try to understand the late time acceleration of the universe by assuming some modification in the geometry of the space and using dynamical system analysis. This technique allows to understand the behavior of the universe…
In cosmology, the cosmic curvature $K$ and the cosmological constant $\Lambda$ are two important parameters, and the values have strong influence on the behavior of the universe. In the context of normal cosmology, under the ordinary…
Understanding the accelerating expansion of the Universe remains a fundamental challenge in modern cosmology. In this paper, we investigate a cosmological model parametrized by a generalized variable deceleration parameter to elucidate the…