Minimal theory of massive gravity

TL;DR

This paper introduces a minimal massive gravity theory with only two propagating degrees of freedom, matching dRGT in some aspects but lacking scalar and vector modes, offering a stable nonlinear cosmological solution.

Contribution

The paper develops a new massive gravity theory with fewer degrees of freedom, eliminating scalar and vector modes at the nonlinear level, and providing a stable self-accelerating cosmology.

Findings

Matches dRGT in background cosmology and tensor perturbations

Lacks scalar and vector gravitational degrees of freedom at nonlinear level

Offers a stable nonlinear completion of self-accelerating solutions

Abstract

We propose a new theory of massive gravity with only two propagating degrees of freedom. After defining the theory in the unitary gauge in the vielbein language, we shall perform a Hamiltonian analysis to count the number of physical degrees of freedom, and then study some phenomenologies. While the homogeneous and isotropic background cosmology and the tensor linear perturbations around it are described by exactly the same equations as those in the de Rham-Gabadadze-Tolley (dRGT) massive gravity, the scalar and vector gravitational degrees of freedom are absent in the new theory at the fully nonlinear level. Hence the new theory provides a stable nonlinear completion of the self-accelerating cosmological solution that was originally found in the dRGT theory.