Note About Consistent Extension of Quasidilaton Massive Gravity

TL;DR

This paper critically examines a proposed extension of quasidilaton massive gravity, revealing the absence of a key constraint that ensures ghost freedom, and proposes a new ghost-free extension.

Contribution

The paper provides a Hamiltonian analysis showing the missing primary constraint in the extension and proposes a new ghost-free formulation.

Findings

The extension lacks the primary constraint for ghost elimination.

Comparison shows differences with original quasidilaton massive gravity.

A new ghost-free extension is proposed.

Abstract

This note is devoted to the Hamiltonian analysis of extension of quasidilaton massive gravity as was proposed recently in [arXiv:1306.5502]. We show that for given formulation of the theory the additional primary constraint that is responsible for the elimination of the Boulware-Deser ghost is missing. We compare this situation with quasidilaton massive gravity. Finally we propose ghost free extension of quasidilaton massive gravity.