Cosmological Non-Linearities as an Effective Fluid
  The universe is smooth on large scales but very inhomogeneous on small
scales. Why is the spacetime on large scales modeled to a good approximation by
the Friedmann equations? Are we sure that small-scale non-linearities do not
induce a large backreaction? Related to this, what is the effective theory that
describes the universe on large scales? In this paper we make progress in
addressing these questions. We show that the effective theory for the
long-wavelength universe behaves as a viscous fluid coupled to gravity:
integrating out short-wavelength perturbations renormalizes the homogeneous
background and introduces dissipative dynamics into the evolution of
long-wavelength perturbations. The effective fluid has small perturbations and
is characterized by a few parameters like an equation of state, a sound speed
and a viscosity parameter. These parameters can be matched to numerical
simulations or fitted from observations. We find that the backreaction of
small-scale non-linearities is very small, being suppressed by the large
hierarchy between the scale of non-linearities and the horizon scale. The
effective pressure of the fluid is always positive and much too small to
significantly affect the background evolution. Moreover, we prove that
virialized scales decouple completely from the large-scale dynamics, at all
orders in the post-Newtonian expansion. We propose that our effective theory be
used to formulate a well-defined and controlled alternative to conventional
perturbation theory, and we discuss possible observational applications.
Finally, our way of reformulating results in second-order perturbation theory
in terms of a long-wavelength effective fluid provides the opportunity to
understand non-linear effects in a simple and physically intuitive way.
