Inflationary perturbation theory is geometrical optics in phase space
  A pressing problem in comparing inflationary models with observation is the
accurate calculation of correlation functions. One approach is to evolve them
using ordinary differential equations ("transport equations"), analogous to the
Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this
approach to the complete set of momentum space correlation functions. A formal
solution can be obtained using raytracing techniques adapted from geometrical
optics. We reformulate inflationary perturbation theory in this language, and
show that raytracing reproduces the familiar "delta N" Taylor expansion. Our
method produces ordinary differential equations which allow the Taylor
coefficients to be computed efficiently. We use raytracing methods to express
the gauge transformation between field fluctuations and the curvature
perturbation, zeta, in geometrical terms. Using these results we give a compact
expression for the nonlinear gauge-transform part of fNL in terms of the
principal curvatures of uniform energy-density hypersurfaces in field space.
