Multi-Metric Gravity via Massive Gravity

TL;DR

This paper introduces a three-metric massive gravity theory predicting a massless graviton decoupled from two massive interacting gravitons, with cosmological solutions resembling de-Sitter space and no flat homogeneous solutions.

Contribution

It generalizes massive gravity to include three dynamical metrics, revealing unique linear and cosmological properties not seen in previous models.

Findings

Predicts a massless spin-2 field decoupled from two massive gravitons

Cosmological solutions exhibit de-Sitter behavior with a mass-dependent cosmological constant

No homogeneous, isotropic, flat solutions exist when one metric is Minkowskian

Abstract

A generalization to the theory of massive gravity is presented which includes three dynamical metrics. It is shown that at the linear level, the theory predicts a massless spin-2 field which is decoupled from the other two gravitons which are massive and interacting. In this regime the matter naturally should be coupled to massless graviton which introduces a preferred metric that is the average of the primary metrics. The cosmological solution of the theory shows the de-Sitter behavior with a function of mass as its cosmological constant. Surprisingly, it lacks any non-trivial solution when one of the metrics is taken to be Minkowskian and seems to enhance the predictions which suggests that there is no homogeneous, isotropic and flat solution for the standard massive cosmology.