The Effective Fluid Approach to Cosmological Nonlinearities:
  Applications to Preheating
  In [arXiv:1004.2488], Baumann et al. present a new formalism for studying
cosmological systems where the characteristic scale of non-linearities is much
smaller than the Hubble scale. By integrating out the short-wavelength modes,
it is possible to obtain an effective theory of long-wavelength perturbations
that is described by an imperfect fluid evolving in an FRW background. As the
long-wavelength perturbations remain small even when the short-scale dynamics
are non-linear, the tools of linear perturbation theory may be applied. The
work in [arXiv:1004.2488] deals only with matter in the form of a pressureless
perfect fluid with zero anisotropic stress, and also assumes that the
short-scale gravitational dynamics are Newtonian. In this work we extend this
formalism to the case of a perfect fluid with pressure, and in particular to
the case of preheating after inflation, where the matter content of the
universe can be modeled by two coupled scalar fields. We discard the assumption
that the short-scale gravitational dynamics are Newtonian. We find that our
results differ from Baumann et al.'s even when the pressure is set to zero,
which suggests that relaxing their assumptions creates appreciable changes in
the long-wavelength effective theory. We derive equations of motion for the
total density perturbation and matter velocities during preheating, as well as
linearized Einstein equations for the long-wavelength metric perturbations. We
also present the equations governing the effective long-wavelength scalar field
dynamics.
