Massive gravity from bimetric gravity

TL;DR

This paper explores the nuanced relationship between massive gravity and bimetric gravity, emphasizing the importance of the limiting process and its implications for cosmological solutions.

Contribution

It clarifies the proper limiting procedure from bimetric to massive gravity, highlighting the constraints and solution continuity issues involved.

Findings

Solutions of bimetric gravity with vanishing kinetic term are also solutions of massive gravity.

Many cosmological solutions are continuous in the parameter space.

The limiting process must avoid constraining the background metric unnecessarily.

Abstract

We discuss the subtle relationship between massive gravity and bimetric gravity, focusing particularly on the manner in which massive gravity may be viewed as a suitable limit of bimetric gravity. The limiting procedure is more delicate than currently appreciated. Specifically, this limiting procedure should not unnecessarily constrain the background metric, which must be externally specified by the theory of massive gravity itself. 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, leading to additional constraints besides the one set of equations of motion naively expected. Thus, since 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, there is not complete continuity in the parameter space of the theory. In particular, we study the massive cosmological solutions which are continuous in the parameter space, showing that many interesting cosmologies belong to this class.