Higher dimensional massive bigravity

Abstract

We study higher dimensional scenarios of massive bigravity, which is a very interesting extension of nonlinear massive gravity since its reference metric is assumed to be full dynamical. In particular, the Einstein field equations along with the following constraint equations for both physical and reference metrics of a five-dimensional massive bigravity will be addressed. Then, we study some well-known cosmological spacetimes such as the Friedmann-Lemaitre-Robertson-Walker, Bianchi type I, and Schwarzschild-Tangherlini metrics for the five-dimensional massive bigravity. As a result, we find that massive graviton terms will serve as effective cosmological constants in both physical and reference sectors if a special scenario, in which reference metrics are chosen to be proportional to physical ones, is considered for all mentioned metrics. Thanks to the constancy property of massive graviton terms, consistent cosmological solutions will be figured out accordingly.