Effective theories for a nonrelativistic field in an expanding universe:
  Induced self-interaction, pressure, sound speed, and viscosity
  A massive, nonrelativistic scalar field in an expanding spacetime is usually
approximated by a pressureless perfect fluid, which leads to the standard
conclusion that such a field can play the role of cold dark matter. In this
paper, we systematically study these approximations, incorporating subleading
corrections. We provide two equivalent effective descriptions of the system,
each of which offers its own advantages and insights: (i) A nonrelativistic
effective field theory (EFT) with which we show that the relativistic
corrections induce an effective self-interaction for the nonrelativistic field.
As a byproduct, our EFT also allows one to construct the exact solution,
including oscillatory behavior, which is often difficult to achieve from the
exact equations. (ii) An effective (imperfect) fluid description, with which we
demonstrate that, for a perturbed Friedmann-Lema\^{i}tre-Robertson-Walker
(FLRW) universe: (a) The pressure is small but nonzero (and positive), even for
a free theory with no tree-level self-interactions. (b) The sound speed of
small fluctuations is also nonzero (and positive), reproducing already known
leading-order results, correcting a subdominant term, and identifying a new
contribution that had been omitted in previous analyses. (c) The fluctuations
experience a negative effective bulk viscosity. The positive sound speed and
the negative bulk viscosity act in favor of and against the growth of
overdensities, respectively. The net effect may be considered a smoking gun for
ultra-light dark matter.
