Infrared Modified Gravity with Dynamical Torsion

TL;DR

This paper explores a modified gravity theory with dynamical torsion, demonstrating consistent propagation of massive spin-2 modes without ghosts in certain backgrounds, extending previous results to more general settings.

Contribution

It generalizes the Fierz--Pauli equation for massive spin-2 fields to backgrounds with arbitrary torsionless Einstein manifolds, showing no additional degrees of freedom or ghosts.

Findings

Number of propagating degrees of freedom remains unchanged in Einstein backgrounds.

No Boulware--Deser ghost appears in de Sitter and anti-de Sitter backgrounds.

Weakly curved backgrounds do not introduce ghosts in the model.

Abstract

We continue the recent study of the possibility of constructing a consistent infrared modification of gravity by treating the vierbein and connection as independent dynamical fields. We present the generalized Fierz--Pauli equation that governs the propagation of a massive spin-2 mode in a model of this sort in the backgrounds of arbitrary torsionless Einstein manifolds. We show explicitly that the number of propagating degrees of freedom in these backgrounds remains the same as in flat space-time. This generalizes the recent result that the Boulware--Deser phenomenon does not occur in de Sitter and anti-de Sitter backgrounds. We find that, at least for weakly curved backgrounds, there are no ghosts in the model. We also briefly discuss the interaction of sources in flat background.