Role of matter in extended quasidilaton massive gravity
  The extended quasidilaton theory is one of the simplest Lorentz-invariant
massive gravity theories which can accommodate a stable self-accelerating
vacuum solution. In this paper we revisit this theory and study the effect of
matter fields. For a matter sector that couples minimally to the physical
metric, we find hints of a Jeans type instability in the IR. In the analogue
k-essence field set-up, this instability manifests itself as an IR ghost for
the scalar field perturbation, but this can be interpreted as a classical
instability that becomes relevant below some momentum scale in terms of matter
density perturbations. We also consider the effect of the background evolution
influenced by matter on the stability of the gravity sector perturbations. In
particular, we address the previous claims of ghost instability in the IR
around the late time attractor. We show that, although the matter-induced
modification of the evolution potentially brings tension to the stability
conditions, one goes beyond the regime of validity of the effective theory well
before the solutions become unstable. We also draw attention to the fact that
the IR stability conditions are also enforced by the existence requirements of
consistent background solutions.
