Massive gravity as a limit of bimetric gravity

TL;DR

This paper explores how massive gravity can be derived as a limit of bimetric gravity, revealing complex interactions between metrics and implications for cosmological solutions.

Contribution

It clarifies the relationship between bimetric and massive gravity, especially how solutions transfer in the limit of vanishing kinetic terms.

Findings

Solutions of bimetric gravity become solutions of massive gravity in the limit.

The interplay between background and foreground metrics affects cosmological solutions.

Not all massive gravity solutions originate from bimetric gravity solutions.

Abstract

Massive gravity may be viewed as a suitable limit of bimetric gravity. The limiting procedure can lead to an interesting interplay between the "background" and "foreground" metrics in a cosmological context. The fact that in bimetric theories one always has two sets of metric equations of motion continues to have an effect even in the massive gravity limit. Thus, solutions of bimetric gravity in the limit of vanishing kinetic term are also solutions of massive gravity, but the contrary statement is not necessarily true.