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

Abstract

We examine the relation between the dynamics of Lema\^ıtre-Tolman-Bondi (LTB) dust models (with and without $\Lambda$) 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.

V2: References added and typos corrected. Version accepted for publication in PRD

References in corpus (9)

• Relativistic cosmology and large-scale structure
• Testing the Void against Cosmological data: fitting CMB, BAO, SN and H0
• Scalar Perturbations on Lemaitre-Tolman-Bondi Spacetimes
• Scale-dependent bias from primordial non-Gaussianity in general relativity
• Observational constraints on the LLTB model
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Cited by in corpus (4)

• Lemaitre-Tolman-Bondi dust solutions in f(R) gravity
• The background Friedmannian Hubble constant in relativistic inhomogeneous cosmology and the age of the Universe
• Inhomogeneous solutions in $f(T,B)$ gravity
• The first non-static inhomogeneous exact solution in $f(T,B)$ gravity