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arXiv · 1412.8404

On spherical dust fluctuations: the exact vs. the perturbative approach

Roberto A. Sussman·Juan Carlos Hidalgo·Peter K. S. Dunsby·Gabriel German
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Abstract

We examine the relation between the dynamics of Lema\^ıtre-Tolman-Bondi (LTB) dust models (with and without $Λ$) and the dynamics of dust perturbations in two of the more familiar formalisms used in cosmology: the metric based Cosmological Perturbation Theory (CPT) and the Covariant Gauge Invariant (GIC) perturbations. For this purpose we recast the evolution of LTB models in terms of a covariant and gauge invariant formalism of local and non-local "exact fluctuations " on a Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) background defined by suitable averages of covariant scalars. We examine the properties of these fluctuations, which can be defined for a confined comoving domain or for an asymptotic domain extending to whole time slices. In particular, the non-local density fluctuation provides a covariant and precise definition for the notion of the "density contrast ". We show that in their linear regime these LTB exact fluctuations (local and non-local) are fully equivalent to the conventional cosmological perturbations in the synchronous-comoving gauge of CPT and to GIC perturbations. As an immediate consequence, we show the time-invariance of the spatial curvature perturbation in a simple form. The present work may provide important theoretical connections between the exact and perturbative (linear or no-linear) approach to the dynamics of dust sources in General Relativity.

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Roberto A. Sussman, Juan Carlos Hidalgo, Peter K. S. Dunsby, Gabriel German. 2015-02-09. On spherical dust fluctuations: the exact vs. the perturbative approach. https://doi.org/10.1103/physrevd.91.063512

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