Anisotropic universes in the ghost-free bigravity

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.