Cosmological Perturbation Theory Using the FFTLog: Formalism and
  Connection to QFT Loop Integrals
  We present a new method for calculating loops in cosmological perturbation
theory. This method is based on approximating a $\Lambda$CDM-like cosmology as
a finite sum of complex power-law universes. The decomposition is naturally
achieved using an FFTLog algorithm. For power-law cosmologies, all loop
integrals are formally equivalent to loop integrals of massless quantum field
theory. These integrals have analytic solutions in terms of generalized
hypergeometric functions. We provide explicit formulae for the one-loop and the
two-loop power spectrum and the one-loop bispectrum. A chief advantage of our
approach is that the difficult part of the calculation is cosmology
independent, need be done only once, and can be recycled for any relevant
predictions. Evaluation of standard loop diagrams then boils down to a simple
matrix multiplication. We demonstrate the promise of this method for
applications to higher multiplicity/loop correlation functions.
