Spatial averaging and apparent acceleration in inhomogeneous spaces

TL;DR

This paper investigates whether inhomogeneous LTB models can mimic cosmic acceleration by analyzing null geodesics and spatial averaging, finding that positive averaged acceleration often conflicts with observations.

Contribution

It provides a detailed analytical derivation of null geodesic equations in LTB models and examines the relationship between spatial averaging and observable acceleration.

Findings

Positive averaged acceleration in LTB models can be incompatible with observations.

LTB models with positive $a_D$ may not reproduce observed luminosity distances.

Positive $a_D$ does not necessarily imply positive apparent acceleration $a^{FLRW}$.

Abstract

As an alternative to dark energy that explains the observed acceleration of the universe, it has been suggested that we may be at the center of an inhomogeneous isotropic universe described by a Lemaitre-Tolman-Bondi (LTB) solution of Einstein's field equations. To test this possibility, it is necessary to solve the null geodesics. In this paper we first give a detailed derivation of a fully analytical set of differential equations for the radial null geodesics as functions of the redshift in LTB models. As an application we use these equaions to show that a positive averaged acceleration $a_D$ obtained in LTB models through spatial averaging can be incompatible with cosmological observations. We provide examples of LTB models with positive $a_D$ which fail to reproduce the observed luminosity distance $D_L(z)$. Since the apparent cosmic acceleration $a^{FLRW}$ is obtained from fitting the observed luminosity distance to a FLRW model we conclude that in general a positive $a_D$ in LTB models does not imply a positive $a^{FLRW}$.