Related papers: Multidimensional Gravity and Cosmology: Exact Solu…
In these lectures my aim is to review enough of conformal differential geometry in four dimensions to give an account of Penrose's conformal cyclic geometry.
We find exact and explicit solutions of the axisymmetric MHD equations of a self-gravitating polytropic gas. These solutions are able to describe a flat (uniform density) subsonic internal core, contracting homologously, of a collapsing…
Cosmic structure simulations have improved enormously over the past decade, both in terms of the resolution which can be achieved, and with the addition of hydrodynamic and other techniques to formerly purely gravitational methods. This is…
Various contributions to the cosmological constant are discussed and confronted with its recent measurement. We briefly review different scenarious -- and their difficulties -- for a solution of the cosmological constant problem.
The paper presents results for deriving closed-form analytic solutions of the evolution of inhomogeneities in a homogeneous spatially flat multicomponent cosmological model. Mathematical methods to derive computable forms of the…
In this paper we present a number of examples of exact solutions for the Friedmann cosmological equation for metric $ F(R) $ gravity model. Emphasis was placed on the possibility of obtaining exact time dependences of the main cosmological…
The cylindrically-symmetric static vacuum equations of Conformal Gravity are solved for the case of additional boost symmetry along the axis. We present the complete family of solutions which describe the exterior gravitational field of…
Nowadays, $f(R)$ theory has been one of the leading modified gravity theories to explain the current accelerated expansion of the universe, without invoking dark energy. It is of interest to find the exact cosmological solutions of $f(R)$…
In this work, exact solutions of static and spherically symmetric space-times are analyzed in f(R) modified theories of gravity coupled to nonlinear electrodynamics. Firstly, we restrict the metric fields to one degree of freedom,…
The long story of the oscillatory approach to the initial cosmological singularity and its more recent incarnation in multidimensional universe models is told.
We show that a number of problems of modern cosmology may be addressed and solved in the framework of multidimensional gravity with high-order curvature invariants, without invoking other fields. As applications of this approach, we mention…
We review analytical solutions of the Einstein equations which are expressed in terms of elementary functions and describe Friedmann-Lema\^itre-Robertson-Walker universes sourced by multiple (real or effective) perfect fluids with constant…
The acoustic equations derived as a linearization of the Euler equations are a valuable system for studies of multi-dimensional solutions. Additionally they possess a low Mach number limit analogous to that of the Euler equations. Aiming at…
We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.
It is commonly stated that we have entered the era of precision cosmology in which a number of important observations have reached a degree of precision, and a level of agreement with theory, that is comparable with many Earth-based physics…
We review Extended Theories of Gravity in metric and Palatini formalism pointing out their cosmological and astrophysical application. The aim is to propose an alternative approach to solve the puzzles connected to dark components.
We present an elementary account of mathematical cosmology through a series of important unsolved problems. We introduce the fundamental notion of `a cosmology' and focus on the issue of singularities as a theme unifying many current,…
We investigate Extended Geometric Trinity of Gravity at both classical and quantum cosmological levels using the minisuperspace approach. Adopting Noether symmetries to select viable models, we examine metric-affine theories of gravity, in…
General relativity becomes vastly simpler in three spacetime dimensions: all vacuum solutions have constant curvature, and the moduli space of solutions can be almost completely characterized. As a result, this lower dimensional setting…
Understanding of the structure evolution in the Universe has been greatly advanced with a rapid progress in high-resolution cosmological simulations. In this contribution, we report a new set of cosmological simulations with $512^3$ ($\sim…