Post-Newtonian cosmological dynamics of plane-parallel perturbations and back-reaction

Abstract

We study the general relativistic non-linear dynamics of self-gravitating irrotational dust in a cosmological setting, adopting the comoving and synchronous gauge, where all the equations can be written in terms of the metric tensor of spatial hyper-surfaces orthogonal to the fluid flow. Performing an expansion in inverse powers of the speed of light, we obtain the post-Newtonian equations, which yield the lowest-order relativistic effects arising during the non-linear evolution. We then specialize our analysis to globally plane-parallel configurations, i.e. to the case where the initial perturbation field depends on a single coordinate. The leading order of our expansion, corresponding to the "Newtonian background", is the Zel'dovich approximation, which, for plane-parallel perturbations in the Newtonian limit, represents an exact solution. This allows us to find the exact analytical form for the post-Newtonian metric, thereby providing the post-Newtonian extension of the Zel'dovich solution: this accounts for some relativistic effects, such as the non-Gaussianity of primordial perturbations. An application of our solution in the context of the back-reaction proposal is eventually given, providing a post-Newtonian estimation of kinematical back-reaction, mean spatial curvature and average scale-factor.

revised to match the version accepted for publication in JCAP

References in corpus (3)

• Unified treatment of cosmological perturbations from super-horizon to small scales
• Applicability of the linearly perturbed FRW metric and Newtonian cosmology
• Exact nonlinear inhomogeneities in $\Lambda$CDM cosmology

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• The background Friedmannian Hubble constant in relativistic inhomogeneous cosmology and the age of the Universe
• Isolating non-linearities of light propagation in inhomogeneous cosmologies
• Periodic boundary conditions and $G_2$ cosmology