Exact Solution to the "Auxiliary Extra Dimension" Model of Massive Gravity

TL;DR

This paper provides an exact solution to the auxiliary extra dimension model of massive gravity, revealing the ghost problem at higher orders and discussing potential modifications to resolve it.

Contribution

It offers an exact solution to the model's equations of motion, clarifying the ghost issue and its order of appearance in the theory.

Findings

Ghost appears at fourth order and beyond

Exact solution clarifies the model's structure

Modifications to fix ghosts require going beyond current framework

Abstract

The "Auxiliary Extra Dimension" model was proposed in order to provide a geometrical interpretation to modifications of general relativity, in particular to non-linear massive gravity. In this context, the theory was shown to be ghost free to third order in perturbations, in the decoupling limit. In this work, we exactly solve the equation of motion in the extra dimension, to obtain a purely 4-dimensional theory. Using this solution, it is shown that the ghost appears at the fourth order and beyond. We explore potential modifications to address the ghost issue and find that their consistent implementation requires going beyond the present framework.