  We explore cosmology in the decoupling limit of a non-linear covariant
extension of Fierz-Pauli massive gravity obtained recently in arXiv:1007.0443.
In this limit the theory is a scalar-tensor model of a unique form defined by
symmetries. We find that it admits a self-accelerated solution, with the Hubble
parameter set by the graviton mass. The negative pressure causing the
acceleration is due to a condensate of the helicity-0 component of the massive
graviton, and the background evolution, in the approximation used, is
indistinguishable from the \Lambda CDM model. Fluctuations about the
self-accelerated background are stable for a certain range of parameters
involved. Most surprisingly, the fluctuation of the helicity-0 field above its
background decouples from an arbitrary source in the linearized theory. We also
show how massive gravity can remarkably screen an arbitrarily large
cosmological constant in the decoupling limit, while evading issues with
ghosts. The obtained static solution is stable against small perturbations,
suggesting that the degravitation of the vacuum energy is possible in the full
theory. Interestingly, however, this mechanism postpones the Vainshtein effect
to shorter distance scales. Hence, fifth force measurements severely constrain
the value of the cosmological constant that can be neutralized, making this
scheme phenomenologically not viable for solving the old cosmological constant
problem. We briefly speculate on a possible way out of this issue.
