Cosmological solutions with massive gravitons in the bigravity theory

Abstract

We present solutions describing homogeneous and isotropic cosmologies in the massive gravity theory with two dynamical metrics recently proposed in arXiv:1109.3515 and claimed to be ghost free. These solutions can be spatially open, closed, or flat, and at early times they are sourced by the perfect fluid, while the graviton mass typically manifests itself at late times by giving rise to a cosmological term. In addition, there are also exotic solutions, for which already at early times, when the matter density is high, the contribution of the graviton mass to the energy density is negative and large enough to screen that of the matter contribution. The total energy can then be negative, which may result in removing the initial singularity. For special parameter values there are also solutions for which the two metrics effectively decouple and evolve independently of each other. In the limit where one of the gravitational coupling constant vanishes, such special solutions reduce to those found in arXiv:1107.5504 within the theory where one of the metrics is flat.