Related papers: Averaging Problem in Cosmology and Macroscopic Gra…
We introduce the notion of general K=-1 Friedman-Lema\^itre (compact) cosmologies and the notion of averaged evolution by means of an averaging map. We then analyze the Friedman-Lema\^itre equations and the role of gravitational energy on…
We apply the variable speed of light into general relativity in order to solve the problems we met in the standard cosmology. We're surprised to find that, the results from the general relativity in cosmology are exactly the same as those…
Averaged inhomogeneous cosmologies lie at the forefront of interest, since cosmological parameters like the rate of expansion or the mass density are to be considered as volume-averaged quantities and only these can be compared with…
In the present article, which is the first part of a work in three parts, we build an equation of quantum gravity. This equation is tensorial, is equivalent to general relativity in vacuum, but differs completely from general relativity…
We review recent progress in the construction of modified gravity models as alternatives to dark energy as well as the development of cosmological tests of gravity. Einstein's theory of General Relativity (GR) has been tested accurately…
Structure occurs over a vast range of scales in the universe. Our large-scale cosmological models are coarse-grained representations of what exists, which have much less structure than there really is. An important problem for cosmology is…
The problem of construction of a continuous (macroscopic) matter model for a given point-like (microscopic) matter distribution in general relativity is formulated. The existing approaches are briefly reviewed and a physical analogy with…
The Special Issue on "Modified Gravity Approaches to the Tensions of $\Lambda$CDM"} in the Universe journal tackles significant challenges faced by the $\Lambda$CDM model, including discrepancies in the Hubble constant, growth rate of…
We have critically compared different approaches to the cosmological constant problem, which is at the edge of elementary particle physics and cosmology. This problem is deeply connected with the difficulties formulating a theory of quantum…
The universe is not isotropic or spatially homogeneous on local scales. The averaging of local inhomogeneities in general relativity can lead to significant dynamical effects on the evolution of the universe and on the interpretation of…
An alternative approach to Einstein's theory of General Relativity (GR) is reviewed, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian…
This is a brief review of the standard model of cosmology. We first introduce the FRW models and their flat solutions for energy fluids playing an important role in the dynamics at different epochs. We then introduce different cosmological…
The general relativistic description of cosmological structure formation is an important challenge from both the theoretical and the numerical point of views. In this paper we present a brief prescription for a general relativistic…
In the framework of the recently proposed models of massive gravity, defined with respect to a de Sitter reference metric, we obtain new homogeneous and isotropic solutions for arbitrary cosmological matter and arbitrary spatial curvature.…
Standard cosmological models rely on an approximate treatment of gravity, utilizing solutions of the linearized Einstein equations as well as physical approximations. In an era of precision cosmology, we should ask: are these approximate…
The averaging problem in general relativity concerns the difficulty of defining meaningful averages of tensor quantities and we consider various aspects of the problem. We first address cosmological backreaction which arises because the…
General relativity marked the beginning of modern cosmology and it has since been at the centre of many of the key developments in this field. In the present review, we discuss the general-relativistic dynamics and perturbations of the…
The field equations of general relativity are shown to derive from the existence of a limit force or of a limit power in nature. The limits have the value of c^4/4G and c^5/4G. The proof makes use of a result by Jacobson. All known…
A spherically symmetric comoving fluid solution of Einstein's equations is adapted for cosmological application by extending the geometry of standard FRW cosmology using a generalised curvature term. The resulting model retains many of the…
Several problems in cosmology and astrophysics are described in which critical phenomena of various types may play a role. These include the organization of the disks of spiral galaxies, various aspects of the problem of structure formation…