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 and of the Bianchi class A, which includes types I, II, ${\mathrm{VI}}_{0}$, ${\mathrm{VII}}_{0}$, VIII, and IX. We assume the Universe to contain a radiation and a nonrelativistic 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 nonvanishing 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 nonrelativistic 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 of a chaotic behavior.