2014/12/31 by Roberto A. Sussman, Juan Carlos Hidalgo, Peter K. S. Dunsby +2
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Classical mechanics #Cosmological perturbation theory #Cosmology #Cosmology and Gravitation Theories #Covariant transformation #Density contrast #Friedmann–Lemaître–Robertson–Walker metric #Gauge theory #General relativity #Mathematical physics #Perturbation (astronomy) #Physics #Quantum mechanics #astro-ph.CO #gr-qc
paper · pdf · doi:10.1103/physrevd.91.063512
V2: References added and typos corrected. Version accepted for publication in PRD
arxiv created 2015/02/09 · openalex publication_date 2015/03/09 · arxiv updated 2015/06/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We examine the relation between the dynamics of Lema\\itre--Tolman--Bondi (LTB) dust models (with and without \mathrm\ensuremathΛ) 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--Lema\\itre--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.