Visser's Massive Gravity Bimetric Theory Revisited

TL;DR

This paper revisits Visser's massive gravity theory, identifying a missing factor in the graviton tensor that affects strong field and cosmological solutions, emphasizing the need for a non-static background metric to replicate ΛCDM cosmology.

Contribution

It corrects the graviton tensor in Visser's theory and clarifies the conditions needed for cosmological solutions, especially the necessity of a non-static background metric.

Findings

A missing multiplicative factor in the graviton tensor was identified.

The correction impacts strong field and cosmological applications.

A non-static background metric is necessary for ΛCDM-like solutions.

Abstract

A massive gravity theory was proposed by Visser in the late nineties. This theory, based on a backgroung metric $b_{\alpha \beta}$ and on an usual dynamical metric $g_{\alpha \beta}$ has the advantage of being free of ghosts as well as discontinuities present in other massive theories proposed in the past. In the present investigation, the equations of Visser's theory are revisited with a particular care on the related conservation laws.\ It will be shown that a multiplicative factor is missing in the graviton tensor originally derived by Visser, which has no incidence on the weak field approach but becomes important in the strong field regime when, for instance, cosmological applications are considered. In this case, contrary to some previous claims found in the literature, we conclude that a non-static background metric is required in order to obtain a solution able to mimic the $\Lambda$CDM cosmology.