  We covariantize the decoupling limit of massive gravity proposed in
arXiv:1011.1232 and study the cosmology of this theory as a proxy, which
embodies key features of the fully non-linear covariant theory. We first
confirm that it exhibits a self-accelerating solution, similar to what has been
found in arXiv:1010.1780, 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
LCDM. For consistency we also compare proxy theories obtained starting from
different frames in the decoupling limit and discuss the possibility of
obtaining a non-representative proxy theory by choosing the wrong starting
frame.
