Spherical dust fluctuations: The exact versus the perturbative approach

Abstract

We examine the relation between the dynamics of Lemaitre-Tolman-Bondi (LTB) dust models (with and without A) 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 nonlocal "exact fluctuations" on a Friedmann-Lemaitre-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 nonlocal 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 nonlocal) 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 nonlinear) approach to the dynamics of dust sources in general relativity.

Dynamics of a spherically symmetric inhomogeneous coupled dark energy model with coupling term proportional to non relatvistic matter

“…In FLRW models, the perturbations evolution is introduced as a first order perturbation correction of the background dynamics and the local J can be obtained perturbatively as well by numerical methods. On the other hand, LTB model is an exact solution of Einstein equations with easy to compute equations provided the spherical symmetry that can a match FLRW background connecting the density fluctuations with respect to the QL counterpart as linear FLRW perturbations with a given set of conditions (see [16] for a detailed description of how this identification can be done in a Λ-CDM LTB metric).…”

“…In particular, the spherically symmetric Lemaître-Tolman-Bondi (LTB) metric QuasiLocal (QL) scalar approach [15] can be used to study a local spherical exact solution that matches the homogeneous FLRW at larger scales and the linear perturbations of the FLRW metric can be related to the LTB fluctuations with respect to the QL scalars defined [16]. LTB metrics are well known in the context of pure dust solutions (see [17] for a review), and also in the context of dust plus a cosmological constant [18,16], but not much work is done in the context of more exotic sources such as DE or CDE [19]. In this sense, we believe that an understanding of the dynamics of the inhomogeneous metrics containing those sources is necessary.…”

The background Friedmannian Hubble constant in relativistic inhomogeneous cosmology and the age of the Universe

“…Updates to many of these models should benefit from an observationally justified estimate of H bg 1 . [See also recent work on averaging of LTB (Sussman et al 2015;Chirinos Isidro et al 2016) and Szekeres models (Bolejko 2009); for evolving sign-of-curvature models, see e.g. Krasinski (1981Krasinski ( , 1982Krasinski ( , 1983Stichel (2016); for averaging using Cartan scalars, see Coley (2010); Kašpar & Svítek (2014 Roukema et al 2013), then, through Eqs.…”

Interactive mixture of inhomogeneous dark fluids driven by dark energy: a dynamical system analysis

“…As shown in [40], the dynamics of LTB metrics in the q-scalar formalism yields (through evolution equations like (12a-12f)) an exact non-linear generalisation of linear gauge invariant cosmological perturbations in the isochronous gauge (for any source compatible with the LTB metric). The advantage of using numerical solutions of (12a-12f) lies in the possibility to examine in the non-linear regime the connection between the assumptions on the CDM-DE interaction mediated by J and observations on structure formation in the galactic and galactic cluster and supercluster scales.…”

“…On the other hand, in [49] the evolution of linear perturbations in a FLRW background sharing our assumptions on CDM, DE and J q leads to the bounds − 0.22 > 3α > − 0.90 to comply with the constraints of CMB anisotropy. These results are specially interesting, since the dynamics of LTB solutions described by q-scalars and their fluctuations can be mapped to linear perturbation on an FLRW background [40]. While the spherical symmetry of LTB models allows for the description of a single structure, the latter can be studied exactly in full nonlinear regime.…”