Effective Field Theory of Gravitating Continuum: Solids, Fluids, and
  Aether Unified
  We investigate the relativistic effective field theory (EFT) describing a
non-dissipative gravitating continuum. In addition to ordinary continua, namely
solids and fluids, we find an extraordinary more symmetric continuum, aether.
In particular, the symmetry of the aether concludes that a homogeneous and
isotropic state behaves like a cosmological constant. We formulate the EFT in
the unitary/comoving gauge in which the dynamical degrees of freedom of the
continuum (phonons) are eaten by the spacetime metric. This gauge choice, which
is interpreted as the Lagrangian description in hydrodynamics, offers a neat
geometrical understanding of continua. We examine a thread-based spacetime
decomposition with respect to the four-velocity of the continuum which is
different from the foliation-based Arnowitt-Deser-Misner one. Our thread-based
decomposition respects the symmetries of the continua and, therefore, makes it
possible to systematically find invariant building blocks of the EFT for each
continuum even at higher orders in the derivative expansion. We also discuss
the linear dynamics of the system and show that both gravitons and phonons
acquire "masses" in a gravitating background.
