A Non-linear Massive Gravity Theory of Geometric Origin

TL;DR

This paper investigates the non-linear degrees of freedom in torsion gravity theories, revealing an increase from five to nine degrees of freedom for the torsion field, which impacts the understanding of massive gravity models.

Contribution

It demonstrates that the number of propagating degrees of freedom in torsion bigravity theories increases non-linearly from five to nine, highlighting a novel non-linear behavior.

Findings

Degrees of freedom increase from five to nine at non-linear order.

Linear theory contains only two physical excitations: a massless and a massive spin-2.

Non-linear interactions significantly alter the propagating degrees of freedom.

Abstract

We study the number of propagating degrees of freedom, at non-linear order, in torsion gravity theories, a class of modified theories of gravity that include a propagating torsion in addition to the metric. We focus on a three-parameter subfamily of theories (``torsion bigravity") that contains, at linear order, only two physical excitations: a massless spin-2 one (with two degrees of freedom) and a massive spin-2 one (with five degrees of freedom). We study the dynamics of the massive spin-2 field in the limit where the torsion field decouples from the metric. The number of degrees of freedom of the torsion field is found to {\it change, at non-linear order, from five to nine}.