Effective field theory of dark matter and structure formation: Semianalytical 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 (Lambda CDM) 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 nonlinear scale similar to 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.CDM 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 similar to 10(-6)c(2)k(2)/H-2. Starting from the linear theory, we calculate corrections to cosmological observables, such as the baryonacoustic- oscillation peak, which we compute semianalytically at one-loop order. Due to the nonzero 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 wavelike and other issues.