Perturbation theory, effective field theory, and oscillations in the
  power spectrum
  We explore the relationship between the nonlinear matter power spectrum and
the various Lagrangian and Standard Perturbation Theories (LPT and SPT). We
first look at it in the context of one dimensional (1-d) dynamics, where 1LPT
is exact at the perturbative level and one can exactly resum the SPT series
into the 1LPT power spectrum. Shell crossings lead to non-perturbative effects,
and the PT ignorance can be quantified in terms of their ratio, which is also
the transfer function squared in the absence of stochasticity. At the order of
PT we work, this parametrization is equivalent to the results of effective
field theory (EFT), and can thus be expanded in terms of the same parameters.
We find that its radius of convergence is larger than the SPT loop expansion.
The same EFT parametrization applies to all SPT loop terms and, if
stochasticity can be ignored, to all N-point correlators. In 3-d, the LPT
structure is considerably more complicated, and we find that LPT models with
parametrization motivated by the EFT exhibit running with $k$ and that SPT is
generally a better choice. Since these transfer function expansions contain
free parameters that change with cosmological model their usefulness for
broadband power is unclear. For this reason we test the predictions of these
models on baryonic acoustic oscillations (BAO) and other primordial
oscillations, including string monodromy models, for which we ran a series of
simulations with and without oscillations. Most models are successful in
predicting oscillations beyond their corresponding PT versions, confirming the
basic validity of the model.
