Cosmology of the Galileon from massive gravity

We covariantize the decoupling limit of massive gravity proposed in [de Rham, G. Gabadadze, and A. J. Tolley, Phys. Rev. Lett. 106, 231101 (2011).] and study the cosmology of this theory as a proxy, which embodies key features of the fully nonlinear covariant theory. We first confirm that it exhibits a self-accelerating solution, similar to what has been found in [C. de Rham, G. Gabadadze, L. Heisenberg, and D. Pirtskhalava, Phys. Rev. D 83, 103516 (2011).], where the Hubble parameter corresponds to the graviton mass. For a certain range of parameters fluctuations relative to the self-accelerating background are stable and form an attractor solution. We also show that a degravitating solution can not be constructed in this covariantized proxy theory in a meaningful way. As for cosmic structure formation, we find that the helicity-0 mode of the graviton causes an enhancement relative to Lambda CDM. For consistency we also compare proxy theories obtained starting from different frames in the decoupling limit and discuss the possibility of obtaining a nonrepresentative proxy theory by choosing the wrong starting frame.