Massive Gravity Simplified: A Quadratic Action

TL;DR

This paper introduces a simplified quadratic formulation of massive gravity, demonstrating that all existing models inherently contain the Boulware-Deser ghost in non-trivial backgrounds.

Contribution

It provides a clear proof that previous massive gravity theories cannot avoid the Boulware-Deser ghost using this new quadratic approach.

Findings

All massive gravity models considered have Boulware-Deser ghost in non-trivial backgrounds

The quadratic formulation simplifies the analysis of ghost presence

Explicit proof of ghost inevitability in existing theories

Abstract

We present a simplified formulation of massive gravity where the Higgs fields have quadratic kinetic term. This new formulation allows us to prove in a very explicit way that all massive gravity theories considered so far inevitably have Boulware-Deser ghost in non-trivial fluctuations of background metric.