Related papers: A Complete Cosmological Solution to the Averaged E…
In the macroscopic gravity approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We present exact cosmological solutions to the…
The averaging problem in cosmology and the approach of macroscopic gravity to resolve the problem is discussed. The averaged Einstein equations of macroscopic gravity are modified on cosmological scales by the macroscopic gravitational…
The theory of macroscopic gravity provides a formalism to average the Einstein field equations from small scales to largest scales in space-time. It is well known that averaging is an operation that does not commute with calculating the…
The averaging problem in general relativity is briefly discussed. A new setting of the problem as that of macroscopic description of gravitation is proposed. A covariant space-time averaging procedure is described. The structure of the…
Schwarzschild's solution to the Einstein Field Equations was one of the first and most important solutions that lead to the understanding and important experimental tests of Einstein's theory of General Relativity. However, Schwarzschild's…
The Einstein theories of space-time and gravity as well the stander cosmology are reconstructed thoroughly in this paper based on flat reference frame. The rational parts of the Einstein theories are reserved while the irrational parts…
We couple a neutral scalar field and a Majorana fermion field to Einstein gravity represented by the Robertson-Walker metric and find a class of exact cosmological solutions.
The Einstein theories of space-time and gravity as well the stander cosmology are reconstructed thoroughly in this paper based on flat reference frame. The rational parts of the Einstein theories are reserved while the irrational parts…
A new approach to tackle Einstein equations for an isotropic and homogeneous Friedmann--Robertson--Walker Universe in the presence of a quintessence scalar field is devised. It provides a way to get a simple exact solution to these…
In the MacDowell-Mansouri formulation of general relativity, the spin connection and coframe variables are incorporated into a single Lie algebra-valued connection called the MacDowell-Mansouri connection, $\omega$. From the curvature form…
It is well-known that spacetime averaging is an operation that does not commute with building the Einstein tensor. In the framework of Macroscopic gravity (MG), a covariant averaging procedure, this non-commutativity gives averaged field…
The problem of corrections to Einstein's equations arising from averaging of inhomogeneities ("backreaction") in the cosmological context, has gained considerable attention recently. We present results of analysing cosmological perturbation…
We prove that the Einstein equations can be solved in a very general form for arbitrary spacetime dimensions and various types of vacuum and non-vacuum cases following a geometric method of anholonomic frame deformations for constructing…
Starting with a field theoretic approach in Minkowski space, the gravitational energy momentum tensor is derived from the Einstein equations in a straightforward manner. This allows to present them as {\it acceleration tensor} = const.…
A consistent approach to Cosmology requires an explicit averaging of the Einstein equations, to describe a homogeneous and isotropic geometry. Such an averaging will in general modify the Einstein equations. The averaging procedure due to…
A quantitative test for the validity of the semi-classical approximation in gravity is given. The criterion proposed is that solutions to the semi-classical Einstein equations should be stable to linearized perturbations, in the sense that…
Through averaging the Einstein equations over transverse gravitational perturbations it is obtained a closed system of two ordinary differential equations describing macroscopic cosmological evolution of the isotropic space-flat Universe…
f(R) gravity is a well-known modification of General Relativity, that can be reduced to a scalar-tensor theory by a conformal transformation (Einstein frame). We study static spherically symmetric (SSS) asymptotically flat vacuum…
A number of recent observations have suggested that the Einstein's theory of general relativity may not be the ultimate theory of gravity. The f(R) gravity model with R being the scalar curvature turns out to be one of the best bet to…
The subject of cosmological backreaction in General Relativity is often approached by coordinate-dependent and metric-based analyses. We present in this letter an averaging formalism for the scalar parts of Einstein's equations that is…