Simple inhomogeneous cosmological (toy) models

TL;DR

This paper explores simple inhomogeneous cosmological models based on the Lemaître-Tolman-Bondi metric, analyzing their dynamics, fitting them to observational data, and discussing their potential to explain cosmic acceleration without dark energy.

Contribution

It provides an analytical study of basic features of inhomogeneous models and assesses their observational viability compared to standard cosmology.

Findings

A local hump model fits supernova data better than a local void.

Best-fit scale for the local hump is about 2 Gpc.

Future redshift-drift measurements could distinguish these models from ΛCDM.

Abstract

Based on the Lema\^itre-Tolman-Bondi (LTB) metric we consider two flat inhomogeneous big-bang models. We aim at clarifying, as far as possible analytically, basic features of the dynamics of the simplest inhomogeneous models and to point out the potential usefulness of exact inhomogeneous solutions as generalizations of the homogeneous configurations of the cosmological standard model. We discuss explicitly partial successes but also potential pitfalls of these simplest models. Although primarily seen as toy models, the relevant free parameters are fixed by best-fit values using the Joint Light-curve Analysis (JLA)-sample data. On the basis of a likelihood analysis we find that a local hump with an extension of almost 2 Gpc provides a better description of the observations than a local void for which we obtain a best-fit scale of about 30 Mpc. Future redshift-drift measurements are discussed as a promising tool to discriminate between inhomogeneous configurations and the $\Lambda$CDM model.