Minimal theory of massive gravity

Abstract

We propose a new theory of massive gravity with only two propagating degrees of freedom. 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. The cosmological solution in the other branch, often called the normal branch, is also rendered stable in the new theory and, for the first time, makes it possible to realize an effective equation-of-state parameter different from (either larger or smaller than) -1 without introducing any extra degrees of freedom.