Nonlinear stability of cosmological solutions in massive gravity
  We investigate nonlinear stability of two classes of cosmological solutions
in massive gravity: isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW)
solutions and anisotropic FLRW solutions. For this purpose we construct the
linear cosmological perturbation theory around axisymmetric Bianchi type--I
backgrounds. We then expand the background around the two classes of solutions,
which are fixed points of the background evolution equation, and analyze linear
perturbations on top of it. This provides a consistent truncation of nonlinear
perturbations around these fixed point solutions and allows us to analyze
nonlinear stability in a simple way. In particular, it is shown that isotropic
FLRW solutions exhibit nonlinear ghost instability. On the other hand,
anisotropic FLRW solutions are shown to be ghost-free for a range of parameters
and initial conditions.
