Can a void mimic the $\Lambda$ in $\Lambda$CDM?

TL;DR

This paper examines whether Lemaître-Tolman-Bondi (LTB) models can mimic the $\Lambda$CDM model's predictions, finding significant observational differences and highlighting the need for additional degrees of freedom in alternative cosmological models.

Contribution

It demonstrates that LTB models with certain assumptions cannot fully replicate $\Lambda$CDM predictions, emphasizing the necessity for more complex models.

Findings

LTB and $\Lambda$CDM models predict diverging Hubble functions at higher redshifts.

LTB models show tension with low-redshift BAO and supernova data.

Including CMB and Lyman-$\alpha$ data favors $\Lambda$CDM over LTB models.

Abstract

We investigate Lema\^itre-Tolman-Bondi (LTB) models, whose early time evolution and bang time are homogeneous and the distance - redshift relation and local Hubble parameter are inherited from the $\Lambda$CDM model. We show that the obtained LTB models and the $\Lambda$CDM model predict different relative local expansion rates and that the Hubble functions of the models diverge increasingly with redshift. The LTB models show tension between low redshift baryon acoustic oscillation and supernova observations and including Lyman-$\alpha$ forest or cosmic microwave background observations only accentuates the better fit of the $\Lambda$CDM model compared to the LTB model. The result indicates that additional degrees of freedom are needed to explain the observations, for example by renouncing spherical symmetry, homogeneous bang time, negligible effects of pressure, or the early time homogeneity assumption.