Critical look at cosmological perturbation theory techniques

Recently, a number of analytic prescriptions for computing the nonlinear matter power spectrum have appeared in the literature. These typically involve resummation or closure prescriptions which do not have a rigorous error control, thus they must be compared with numerical simulations to assess their range of validity. We present a direct side-by-side comparison of several of these analytic approaches, using a suite of high-resolution N-body simulations as a reference, and discuss some general trends. All of the analytic results correctly predict the behavior of the power spectrum at the onset of nonlinearity, and improve upon a pure linear theory description at very large scales. All of these theories fail at sufficiently small scales. At low redshift the dynamic range in scale where perturbation theory is both relevant and reliable can be quite small. We also compute for the first time the two-loop contribution to standard perturbation theory for cold dark matter models, finding improved agreement with simulations at large redshift. At low redshifts however the two-loop term is larger than the one-loop term on quasilinear scales, indicating a breakdown of the perturbation expansion. Finally, we comment on possible implications of our results for future studies. A software package implementing the methods presented here is available at http://mwhite.berkeley.edu/Copter.