Massive gravity: a General Analysis

TL;DR

This paper performs a comprehensive Hamiltonian analysis of massive gravity, identifying the most general potential form that propagates five degrees of freedom non-perturbatively, including new solutions with promising phenomenological features.

Contribution

It derives the general form of the potential V in massive gravity ensuring five degrees of freedom and discovers new solutions with healthy phenomenological properties.

Findings

Recovered known Lorentz invariant massive gravity

Discovered new classes of solutions with high UV cutoff

Identified potentials with weak coupling in the solar system

Abstract

Massive gravity can be described by adding to the Einstein-Hilbert action a function V of metric components. By using the Hamiltonian canonical analysis, we find the most general form of V such that five degrees of freedom propagate non perturbatively. The construction is based on a set of differential equations for $V$, that remarkably can be solved in terms of two arbitrary functions. Besides recovering the known "Lorentz invariant" massive gravity theory, we find an entirely new class of solutions, with healthy features on the phenomenological side, in particular they are weakly coupled in the solar system and have a high ultraviolet cutoff Lambda_2=(m M_pl)^(1/2), where m is the graviton mass scale.