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

TL;DR

This work completes the Hamiltonian analysis of a specific non-linear massive gravity model, identifying a primary constraint $\mathcal{C}$ and a secondary constraint $\mathcal{C}^{II}$ that form a second-class pair and remove the extra scalar (ghost) mode. The gravitational sector constraints $\mathcal{H}_T$ and $\mathcal{H}_i$ remain first class, preserving diffeomorphism invariance, while the scalar constraints enforce a nontrivial closure of the constraint surface. The resulting count of physical degrees of freedom matches that of massive gravity, with $N_{p.d}=10$ in phase space (i.e., 10 physical degrees of freedom), confirming ghost freedom for the analyzed model. The analysis provides an independent cross-check without introducing auxiliary fields, complementing prior results in the literature.

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.