# Bi-gravity with a single graviton

## TL;DR

This paper studies a bi-gravity model with a single graviton, showing it aligns with general relativity at linear level and exploring the nature of additional degrees of freedom without introducing a massive graviton or ghost.

## Contribution

It introduces a bi-gravity model with a unique formalism and analyzes its degrees of freedom, revealing it propagates only one graviton and proposing a deformation with three degrees of freedom.

## Key findings

- Linearization agrees with general relativity on many backgrounds
- Additional degrees of freedom do not include a massive graviton or Boulware-Deser ghost
- A foliation-preserving deformation introduces three degrees of freedom

## Abstract

We analyze a bi-gravity model based on the first order formalism, having as fundamental variables two tetrads but only one Lorentz connection. We show that on a large class of backgrounds its linearization agrees with general relativity. At the non-linear level, additional degrees of freedom appear, and we reveal the mechanism hiding them around the special backgrounds. We further argue that they do not contain a massive graviton, nor the Boulware-Deser ghost. The model thus propagates only one graviton, whereas the nature of the additional degrees of freedom remains to be investigated. We also present a foliation-preserving deformation of the model, which keeps all symmetries except time diffeomorphisms and has three degrees of freedom.