Visser’s massive graviton bimetric theory revisited

A massive gravity theory was proposed by Visser in the late 1990s. This theory, based on a background 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 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 nonstatic background metric is required in order to obtain a solution able to mimic the $\Lambda \mathrm{CDM}$ cosmology.