Hidden Ghost in Massive gravity

TL;DR

This paper investigates a version of massive gravity with an infinite square root expansion, revealing a hidden ghost mode due to the vanishing Hessian determinant, which introduces an unphysical tachyonic state.

Contribution

It demonstrates that eliminating one scalar field in this massive gravity model leads to a nonlinear ghost and an extra tachyonic mode, highlighting a fundamental instability.

Findings

Hessian determinant vanishes, indicating a hidden ghost.

Elimination of scalar fields introduces extra time derivatives.

Constraint analysis reveals a tachyonic instability.

Abstract

The Hessian's determinant for a version of massive gravity given by an infinite expansion of a square root function of the induced metric, vanishes. We show that it allows us to eliminate one of four scalar fields used to generate the graviton mass. This, however, gives rise to the appearance of extra terms in the action with the squared time derivative of the metric, thus signaling that a nonlinear ghost survives.We demonstrate this phenomenon considering a simple system with constraint, which is supposed to reduces the number of physical degrees of freedom, however, we explicitly show how the constraint forces the metric to propagate an extra tachyonic state.