Chiral gravity as a covariant formulation of massive gravity

TL;DR

This paper introduces a covariant nonlinear formulation of massive gravity by extending Einstein gravity with two vielbeins, resulting in a theory with a massless and a massive graviton, and explores its unique properties and limits.

Contribution

It provides a covariant nonlinear completion of the Fierz-Pauli mass term using a two-vielbein approach with chiral spin-connections, a novel framework for massive gravity.

Findings

Spectrum includes massless and massive gravitons with FP mass term.

Requires fine-tuning to recover Minkowski background.

In certain limits, only the massive graviton couples to matter.

Abstract

We present a covariant nonlinear completion of the Fierz-Pauli (FP) mass term for the graviton. The starting observation is that the FP mass is immediately obtained by expanding the cosmological constant term, i.e. the determinant of the vielbein, around Minkowski space to second order in the vielbein perturbations. Since this is an unstable expansion in the standard case, we consider an extended theory of gravity which describes two vielbeins that give rise to chiral spin--connections (consequently, fermions of a definite chirality only couple to one of the gravitational sectors). As for Einstein gravity with a cosmological constant, a single fine-tuning is needed to recover a Minkowski background; the two sectors then differ only by a constant conformal factor. The spectrum of this theory consists of a massless and a massive graviton, with FP mass term. The theory possesses interesting limits in which only the massive graviton is coupled to matter at the linearized level.