Translation invariant time-dependent massive gravity: Hamiltonian analysis

TL;DR

This paper performs a Hamiltonian analysis of translation invariant massive gravity, showing that only dRGT mass terms yield the correct number of degrees of freedom, and explores the system's dynamical evolution.

Contribution

It demonstrates that only dRGT mass terms produce five propagating degrees of freedom in translation invariant massive gravity.

Findings

dRGT mass terms are unique in yielding 5 degrees of freedom

Hamiltonian analysis confirms the dynamical consistency of these terms

The study clarifies the structure of massive gravity in a simplified setting

Abstract

The canonical structure of the massive gravity in the first order moving frame formalism is studied. We work in the simplified context of translation invariant fields, with mass terms given by general non-derivative interactions, invariant under the diagonal Lorentz group, depending on the moving frame as well as a fixed reference frame. We prove that the only mass terms which give 5 propagating degrees of freedom are the dRGT mass terms, namely those which are linear in the lapse. We also complete the Hamiltonian analysis with the dynamical evolution of the system.