Self-accelerating Massive Gravity: Time for Field Fluctuations
  The ghost-free theory of massive gravity has exact solutions where the
effective stress energy generated by the graviton mass term is a cosmological
constant for any isotropic metric. Since they are exact, these solutions mimic
a cosmological constant in the presence of any matter-induced isotropic metric
perturbation. In the Stueckelberg formulation, this stress energy is carried
entirely by the spatial Stueckelberg field. We show that any stress energy
carried by fluctuations in the spatial field away from the exact solution
always decays away in an expanding universe. However, the dynamics of the
spatial Stueckelberg field perturbation depend on the background temporal
Stueckelberg field, which is equivalent to the unitary gauge time coordinate.
This dependence resolves an apparent conflict in the existing literature by
showing that there is a special unitary time choice for which the field
dynamics and energy density perturbations vanish identically. In general, the
isotropic system has a single dynamical degree of freedom requiring two sets of
initial data; however, only one of these initial data choices will affect the
observable metric. Finally, we construct cosmological solutions with a
well-defined perturbative initial value formulation and comment on alternate
solutions that evolve to singularities.
