Higher dimensional massive bigravity

TL;DR

This paper explores higher-dimensional massive bigravity, deriving Einstein equations and analyzing cosmological solutions like FLRW, Bianchi I, and Schwarzschild-Tangherlini metrics, revealing graviton terms act as effective cosmological constants under certain conditions.

Contribution

It extends massive bigravity to five dimensions and investigates cosmological solutions with proportional metrics, highlighting the role of graviton terms as effective cosmological constants.

Findings

Massive graviton terms act as effective cosmological constants.

Consistent solutions are found for proportional metrics.

The framework applies to various cosmological spacetimes.

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.