Non-Linear Massive Gravity with Additional Primary Constraint and Absence of Ghosts

TL;DR

This paper completes the Hamiltonian analysis of a specific non-linear massive gravity model, identifying constraints that eliminate ghosts and confirming the physical degrees of freedom match those expected for massive gravity.

Contribution

It provides a detailed Hamiltonian analysis, identifying primary and secondary constraints as second class and confirming the absence of ghost modes in the model.

Findings

Primary and secondary constraints are second class, eliminating the scalar ghost.

Remaining constraints are first class, preserving diffeomorphism invariance.

Number of physical degrees of freedom matches massive gravity expectations.

Abstract

We complete the Hamiltonian analysis of specific model of non-linear massive gravity that was started in arXiv:1112.5267. We identify the primary constraint and corresponding secondary constraint. We show that they are the second class constraints and hence they lead to the elimination of the additional scalar mode. We also find that the remaining constraints are the first class constraints with the structure that corresponds to the manifestly diffeomorphism invariant theory. Finally we determine the number of physical degrees of freedom and we show that it corresponds to the number of physical modes of massive gravity.