The Effective Field Theory of Dark Matter and Structure Formation:
  Semi-Analytical Results
  Complimenting recent work on the effective field theory of cosmological large
scale structures, here we present detailed approximate analytical results and
further pedagogical understanding of the method. We start from the
collisionless Boltzmann equation and integrate out short modes of a dark
matter/dark energy dominated universe (LambdaCDM) whose matter is comprised of
massive particles as used in cosmological simulations. This establishes a long
distance effective fluid, valid for length scales larger than the non-linear
scale ~ 10 Mpc, and provides the complete description of large scale structure
formation. Extracting the time dependence, we derive recursion relations that
encode the perturbative solution. This is exact for the matter dominated era
and quite accurate in LambdaCDM also. The effective fluid is characterized by
physical parameters, including sound speed and viscosity. These two fluid
parameters play a degenerate role with each other and lead to a relative
correction from standard perturbation theory of the form ~ 10^{-6}c^2k^2/H^2.
Starting from the linear theory, we calculate corrections to cosmological
observables, such as the baryon-acoustic-oscillation peak, which we compute
semi-analytically at one-loop order. Due to the non-zero fluid parameters, the
predictions of the effective field theory agree with observation much more
accurately than standard perturbation theory and we explain why. We also
discuss corrections from treating dark matter as interacting or wave-like and
other issues.
