Related papers: Metric Renormalization in General Relativity
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…
This thesis is a review of backreaction, which is a possible alternative to dark energy and modified gravity. We describe in detail the 3+1 covariant formalism and Frobenius' theorem. We present the averaging procedure developed by Buchert,…
The cosmological backreaction arises when one directly averages the Einstein equations to recover an effective Robertson-Walker cosmology, rather than assuming a background a priori. While usually discussed in the context of dark energy,…
One of the outstanding problems in general relativistic cosmology is that of the averaging. That is, how the lumpy universe that we observe at small scales averages out to a smooth Friedmann-Lemaitre-Robertson-Walker (FLRW) model. The root…
The construction of an averaged theory of gravity based on Einstein's General Relativity is very difficult due to the non-linear nature of the gravitational field equations. This problem is further exacerbated by the difficulty in defining…
Averaging in general relativity is a complicated operation, due to the general covariance of the theory and the non-linearity of Einstein's equations. The latter of these ensures that smoothing spacetime over cosmological scales does not…
We generalize and simplify an earlier approach. In three dimensions we present the most general averaging formula in lowest order which respects the requirements of covariance. It involves a bitensor, made up of a basis of six tensors, and…
In the covariant averaging scheme of macroscopic gravity, the process of averaging breaks the metricity of geometry. We reinterpret the back-reaction within macroscopic gravity in terms of the non-metricity of averaged geometry. This…
For the study of cosmological backreacktion an avaragng procedure is required. In this work a covariant and gauge invariant averaging formalism for finite volumes will be developed. This averaging will be applied to the scalar parts of…
A regularization procedure, that allows one to relate singularities of curvature to those of the Einstein tensor without some of the shortcomings of previous approaches, is proposed. This regularization is obtained by requiring that (i) the…
Previous work in the literature had built a formalism for spatially averaged equations for the scale factor, giving rise to an averaged Raychaudhuri equation and averaged Hamiltonian constraint, which involve a backreaction source term. The…
We present a formalism for spatial averaging in cosmology applicable to general spacetimes and coordinates, and allowing the easy incorporation of a wide variety of matter sources. We apply this formalism to a…
This thesis deals with the averaging problem in cosmology, which has gained considerable interest in recent years, and is concerned with correction terms (after averaging inhomogeneities) that appear in the Einstein equations when working…
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…
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…
Cosmology relies on a coarse-grained description of the universe, assumed to be valid on large length scales. However, the nonlinearity of general relativity makes coarse-graining extremely difficult. We here address this problem by…
One possible explanation for the present observed acceleration of the Universe is the breakdown of homogeneity and isotropy due to the formation of non-linear structures. How inhomogeneities affect the averaged cosmological expansion rate…
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 study the averaging problem within the class of…
It is known that any explicit averaging scheme of the type essential for describing the large scale behaviour of the Universe, must necessarily yield corrections to the Einstein equations applied in the Cosmological setting. The question of…
The Universe is homogeneous and isotropic on large scales, so on those scales it is usually modelled as a Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) space-time. The non-linearity of the Einstein field equations raises concern over…