Anisotropic universes in the ghost-free bigravity

TL;DR

This paper investigates anisotropic cosmological models within ghost-free bigravity theory, revealing that such universes tend to retain anisotropies at late times and exhibit complex singularity behaviors, including chaos in Bianchi IX models.

Contribution

It provides the first detailed analysis of Bianchi cosmologies in ghost-free bigravity, highlighting anisotropy evolution and singularity structures in these models.

Findings

Anisotropies decay slower than in General Relativity.

Late-time universe approaches a state with persistent anisotropies.

Bianchi IX models exhibit chaotic Kasner-like singularity behavior.

Abstract

We study Bianchi cosmologies in the ghost-free bigravity theory assuming both metrics to be homogeneous and anisotropic, of the Bianchi class A, which includes types I,II,VI$_0$,VII$_0$,VIII, and IX. We assume the universe to contain a radiation and a non-relativistic matter, with the cosmological term mimicked by the graviton mass. We find that, for generic initial values leading to a late-time self-acceleration, the universe approaches a state with non-vanishing anisotropies. The anisotropy contribution to the total energy density decreases much slower than in General Relativity and shows the same falloff rate as the energy of a non-relativistic matter. The solutions show a singularity in the past, and in the Bianchi IX case the singularity is approached via a sequence of Kasner-like steps, which is characteristic for a chaotic behavior.