Degrees of Freedom in Massive Gravity

TL;DR

This paper systematically analyzes the degrees of freedom in massive gravity using Hamiltonian formalism, deriving conditions for having only five propagating modes and exploring solutions to these conditions.

Contribution

It provides a nonperturbative, background-independent framework to determine the conditions for consistent massive gravity theories with five degrees of freedom.

Findings

Derived differential equations for the deforming potential

Identified restrictive conditions for five degrees of freedom

Found multiple solutions satisfying the conditions

Abstract

We study in a systematic way a generic nonderivative (massive) deformation of general relativity using the Hamiltonian formalism. The number of propagating degrees of freedom is analyzed in a nonperturbative and background independent way. We show that the condition of having only five propagating degrees of freedom can be cast in a set of differential equations for the deforming potential. Though the conditions are rather restrictive, many solutions can be found.