Anisotropically expanding universe in massive gravity

Abstract

We study the cosmological implications of a ghost-free nonlinear massive gravity theory with a cosmological constant. We find that the massive terms serve as an effective cosmological constant for a large class of metric spaces with a compatible fiducial metric associated with the massive terms. A specific solution is solved as an example for this model under the Bianchi type I space and a compatible Bianchi type I fiducial metric. A stability analysis indicates that this set of solutions tends to be stable. Nonetheless, the anisotropically expanding solution will, in general, turn unstable when an additional scalar field with negative kinetic energy is introduced.