FFT-PT: Reducing the two-loop large-scale structure power spectrum to
  low-dimensional radial integrals
  Modeling the large-scale structure of the universe on nonlinear scales has
the potential to substantially increase the science return of upcoming surveys
by increasing the number of modes available for model comparisons. One way to
achieve this is to model nonlinear scales perturbatively. Unfortunately, this
involves high-dimensional loop integrals that are cumbersome to evaluate.
Trying to simplify this, we show how two-loop (next-to-next-to-leading order)
corrections to the density power spectrum can be reduced to low-dimensional,
radial integrals. Many of those can be evaluated with a one-dimensional Fast
Fourier Transform, which is significantly faster than the five-dimensional
Monte-Carlo integrals that are needed otherwise. The general idea of this
FFT-PT method is to switch between Fourier and position space to avoid
convolutions and integrate over orientations, leaving only radial integrals.
This reformulation is independent of the underlying shape of the initial linear
density power spectrum and should easily accommodate features such as those
from baryonic acoustic oscillations. We also discuss how to account for halo
bias and redshift space distortions.
