A critical look at cosmological perturbation theory techniques
  Recently a number of analytic prescriptions for computing the non-linear
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
non-linearity, 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 2-loop
contribution to standard perturbation theory for CDM models, finding improved
agreement with simulations at large redshift. At low redshifts however the
2-loop term is larger than the 1-loop term on quasi-linear scales, indicating a
breakdown of the perturbation expansion. Finally, we comment on possible
implications of our results for future studies.
