Massive Gravity: Resolving the Puzzles

TL;DR

This paper investigates how massive gravity theories transition smoothly to General Relativity below a certain scale, focusing on the role of scalar fields in giving mass to the graviton and the dependence of the Vainshtein scale on the action used.

Contribution

It analyzes the massless limit of Higgs gravity, determines the Vainshtein scale, and demonstrates the smooth transition to General Relativity depending on scalar field actions.

Findings

Massive gravity smoothly approaches General Relativity below the Vainshtein scale.

The Vainshtein scale varies with the scalar field action.

The transition depends on the scalar fields' expectation values.

Abstract

We consider the massless limit of Higgs gravity, where the graviton becomes massive when the scalar fields acquire expectation values. We determine the Vainshtein scale and prove that massive gravity smoothly goes to General Relativity below this scale. We find that the Vainshtein scale depends on the particular action of scalar fields used to give mass to the graviton.