A gradient expansion for cosmological backreaction

Journal of Cosmology and Astroparticle Physics (Impact Factor: 6.04). 12/2011; 2012(03). DOI: 10.1088/1475-7516/2012/03/026
Source: arXiv

ABSTRACT We address the issue of cosmological backreaction from non-linear structure
formation by constructing an approximation for the time evolved metric of a
dust dominated universe based on a gradient expansion. Our metric begins as a
perturbation of a flat Friedmann-Robertson-Walker state described by a nearly
scale invariant, Gaussian, power-law distribution, and evolves in time until
non-linear structures have formed. After describing and attempting to control
for certain complications in the implementation of this approach, this metric
then forms a working model of the universe. We numerically calculate the
evolution of the average scale factor in this model and hence the backreaction.
We argue that, despite its limitations, this model is more realistic than
previous models that have confronted the issue of backreaction. We find that
the \emph{instantaneous} effects of backreaction in this model could be as
large as $\sim10%$ of the background. This suggests that a proper understanding
of the \emph{cumulative} effects of backreaction could be crucial for precision
cosmology and any future exploration of the dark sector.

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    ABSTRACT: Current cosmological observations, when interpreted within the framework of a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) model, strongly suggest that the Universe is entering a period of accelerating expansion. This is often taken to mean that the expansion of space itself is accelerating. In a general spacetime, however, this is not necessarily true. We attempt to clarify this point by considering a handful of local and nonlocal measures of acceleration in a variety of inhomogeneous cosmological models. Each of the chosen measures corresponds to a theoretical or observational procedure that has previously been used to study acceleration in cosmology, and all measures reduce to the same quantity in the limit of exact spatial homogeneity and isotropy. In statistically homogeneous and isotropic spacetimes, we find that the acceleration inferred from observations of the distance-redshift relation is closely related to the acceleration of the spatially averaged universe, but does not necessarily bear any resemblance to the average of the local acceleration of spacetime itself. For inhomogeneous spacetimes that do not display statistical homogeneity and isotropy, however, we find little correlation between acceleration inferred from observations and the acceleration of the averaged spacetime. This shows that observations made in an inhomogeneous universe can imply acceleration without the existence of dark energy.
    Physical review D: Particles and fields 05/2012; 85(10).
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    ABSTRACT: Kinematical and dynamical properties of a generic inhomogeneous cosmological model, spatially averaged with respect to free-falling (generalized fundamental) observers, are investigated for the matter model irrotational dust. Paraphrasing a previous Newtonian investigation, we present a relativistic generalization of a backreaction model based on volume-averaging the Relativistic Zeldovich Approximation. In this model we investigate the effect of kinematical backreaction on the evolution of cosmological parameters as they are defined in an averaged inhomogeneous cosmology, and we show that the backreaction model interpolates between orthogonal symmetry properties by covering subcases of the plane-symmetric solution, the Lemaitre-Tolman-Bondi solution and the Szekeres solution. We so obtain a powerful model that lays the foundations for quantitatively addressing curvature inhomogeneities as they would be interpreted as Dark Energy or Dark Matter in a quasi-Newtonian cosmology. The present model, having a limited architecture due to an assumed FLRW background, is nevertheless capable of replacing 1/4 of the needed amount for Dark Energy on domains of 200 Mpc in diameter for typical (one-sigma) fluctuations in a CDM initial power spectrum. However, the model is far from explaining Dark Energy on larger scales (spatially), where a 6% effect on 400 Mpc domains is identified that can be traced back to an on average negative intrinsic curvature today. One drawback of the quantitative results presented is the fact that the epoch when backreaction is effective on large scales and leads to volume acceleration lies in the future. We discuss this issue in relation to the initial spectrum, the Dark Matter problem, the coincidence problem, and the fact that large-scale Dark Energy is an effect on the past light cone (not spatial), and we pinpoint key elements of future research.
    Physical review D: Particles and fields 03/2013; 87(12).
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    ABSTRACT: Numerical N-body simulations of large scale structure formation in the universe are based on Newtonian gravity. However, according to our current understanding, the most correct theory of gravity is general relativity. It is therefore important to understand which degrees of freedom and which features are lost when the relativistic universe is approximated, or rather replaced, by a Newtonian one. This is the main purpose of our investigation. We first define Newtonian cosmology and we give an overview on general relativity, both in its standard and covariant formulations. We show how the two theories deal with inhomogeneous cosmological models and we introduce the backreaction conjecture. Then we review on how Newtonian gravity and general relativity relate to each other in the fully non-linear regime. For this purpose we discuss frame theory. We carry out the same investigation also in the weak-field, small-velocity limit of general relativity, and we derive the Newtonian limit resorting to the framework of post-Newtonian cosmology. Finally we remark that there are solutions of Newtonian gravity which do not have any relativistic counterpart.


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