Consistent metric combinations in cosmology of massive bigravity

TL;DR

This paper explores various metric configurations in massive bigravity cosmology, identifying specific consistent combinations beyond the standard FLRW assumptions to address stability issues in cosmological solutions.

Contribution

It systematically analyzes non-standard metric combinations in bigravity, revealing which configurations yield stable, consistent cosmological solutions.

Findings

Only certain FLRW-Lemaître, LTB-LTB, and FLRW-Bianchi I combinations are consistent.

Generalized geometries can potentially resolve stability issues in bigravity models.

Some metric configurations do not lead to viable solutions.

Abstract

Massive bigravity models are interesting alternatives to standard cosmology. In most cases, however, these models have been studied for a simplified scenario in which both metrics take homogeneous and isotropic forms [Friedmann-Lema\^itre-Robertson-Walker (FLRW)] with the same spatial curvatures. The interest to consider more general geometries arises, in particular, in view of the difficulty so far encountered in building stable cosmological solutions with homogeneous and isotropic metrics. Here we consider a number of cases in which the two metrics take more general forms, namely FLRW with different spatial curvatures---Lema\^itre, Lema\^itre-Tolman-Bondi (LTB), and Bianchi I---as well as cases where only one metric is linearly perturbed. We discuss possible consistent combinations and find that only some special cases of FLRW--Lema\^itre, LTB--LTB, and FLRW--Bianchi I combinations give consistent, nontrivial solutions.