FRW Cosmology in Ghost Free Massive Gravity

TL;DR

This paper analyzes FRW cosmology within ghost-free massive gravity by promoting the auxiliary metric to a dynamical field (bigravity). The authors derive two cosmological branches from Bianchi identities: one yields standard FRW with an effective cosmological constant set by the graviton mass, and the other yields FRW with an additional gravitational-fluid component whose dynamics are governed by the ratio $\xi=\omega/a$ of the two conformal factors. At early times, large $\xi$ can lead to non-GR behavior, while small $\xi$ recovers GR-like evolution and a late-time de Sitter attractor; spatial curvature analyses show that nontrivial curvature requires careful handling of the two metrics. The results support bigravity as a viable framework for massive gravity cosmology and motivate perturbative studies to assess stability and observational viability.

Abstract

We study FRW homogeneous cosmological solutions in the recently found ghost free massive gravity. In previous works it was shown that when the additional extra metric, needed to generate the mass term, is taken as non-dynamical and flat, no homogeneous FRW cosmology exists. We show that, when the additional metric is a dynamical field, a perfectly safe FRW universe exists. FRW solutions fall in two branches. In the first branch the massive deformation is equivalent to an effectively generated cosmological constant whose scale is determined by the graviton mass. The second branch is quite rich: we have FRW cosmology in the presence of a "gravitational" fluid. The control parameter xi is the ratio of the two conformal factors. When xi is large, generically the cosmological evolution greatly differs from GR at the early time. In the small xi region, the evolution is similar to GR and the universe flows at late time toward an attractor represented by a dS phase.