Massive and modified gravity as self-gravitating media
  We study the effective field theory that describes the low-energy physics of
self-gravitating media. The field content consists of four derivatively coupled
scalar fields that can be identified with the internal comoving coordinates of
the medium. Imposing SO(3) internal spatial invariance, the theory describes
supersolids. Stronger symmetry requirements lead to superfluids, solids and
perfect fluids, at lowest order in derivatives. In the unitary gauge, massive
gravity emerges, being thus the result of a continuous medium propagating in
spacetime. Our results can be used to explore systematically the effects and
signatures of modifying gravity consistently at large distances. The dark
sector is then described as a self-gravitating medium with dynamical and
thermodynamic properties dictated by internal symmetries. These results
indicate that the divide between dark energy and modified gravity, at large
distance scales, is simply a gauge choice.
