Evolution of linear perturbations in Lemaître-Tolman-Bondi void models

Abstract

We study the evolution of linear perturbations in a Lemaître-Tolman-Bondi (LTB) void model with realistic cosmological initial conditions. Linear perturbation theory in LTB models is substantially more complicated than in standard Friedmann universes as the inhomogeneous background causes gauge-invariant perturbations to couple at first order. As shown by Clarkson et al. (2009), the evolution is constrained by a system of linear partial differential equations which need to be integrated numerically. We present a new numerical scheme using finite element methods to solve this equation system and generate scalar initial conditions based on Gaussian random fields with an underlying power spectrum for the Bardeen potential. After spherical harmonic decomposition, the initial fluctuations are propagated in time and estimates of angular power spectra of each gauge invariant variable are computed as functions of redshift. This allows to analyse the coupling strength in a statistical way. We find significant couplings up to $25\%$ for large and deep voids of Gpc scale as required to fit the distance redshift relations of SNe.

39 pages, typos corrected, accepted for publication in JCAP

References in corpus (18)

• Relativistic cosmology and large-scale structure
• Confronting Lemaitre-Tolman-Bondi models with Observational Cosmology
• Lemaitre-Tolman-Bondi model and accelerating expansion
• A Test of the Copernican Principle
• CMB anisotropies seen by an off-center observer in a spherically symmetric inhomogeneous universe
• Looking the void in the eyes - the kSZ effect in LTB models
• Can we avoid dark energy?
• Testing the Void against Cosmological data: fitting CMB, BAO, SN and H0
• Scalar Perturbations on Lemaitre-Tolman-Bondi Spacetimes
• Precision cosmology defeats void models for acceleration
• The radial BAO scale and Cosmic Shear, a new observable for Inhomogeneous Cosmologies
• Linear kinetic Sunyaev-Zel'dovich effect and void models for acceleration
• Observational constraints on the LLTB model
• Probing spatial homogeneity with LTB models: a detailed discussion
• Galaxy correlations and the BAO in a void universe: structure formation as a test of the Copernican Principle
• Spatial and temporal tuning in void models for acceleration
• Conserved Quantities in Lemaitre-Tolman-Bondi Cosmology
• Comparison of two approximation schemes for solving perturbations in a LTB cosmological model

Cited by in corpus (2)

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