Phases of massive gravity

We systematically study the most general Lorentz-violating graviton massinvariant under three-dimensional Eucledian group using the explicitlycovariant language. We find that at general values of mass parameters themassive graviton has six propagating degrees of freedom, and some of them areghosts or lead to rapid classical instabilities. However, there is a number ofdifferent regions in the mass parameter space where massive gravity can bedescribed by a consistent low-energy effective theory with cutoff$\sim\sqrt{mM_{Pl}}$ free of rapid instabilities and vDVZ discontinuity. Eachof these regions is characterized by certain fine-tuning relations between massparameters, generalizing the Fierz--Pauli condition. In some cases the requiredfine-tunings are consequences of the existence of the subgroups of thediffeomorphism group that are left unbroken by the graviton mass. We found twonew cases, when the resulting theories have a property of UV insensitivity,i.e. remain well behaved after inclusion of arbitrary higher dimensionoperators without assuming any fine-tunings among the coefficients of theseoperators, besides those enforced by the symmetries. These theories can bethought of as generalizations of the ghost condensate model with a smallerresidual symmetry group. We briefly discuss what kind of cosmology can oneexpect in massive gravity and argue that the allowed values of the gravitonmass may be quite large, affecting growth of primordial perturbations,structure formation and, perhaps, enhancing the backreaction of inhomogeneitieson the expansion rate of the Universe.Comment: 36 pages, 1 figur