Moment transport equations for the primordial curvature perturbation
  In a recent publication, we proposed that inflationary perturbation theory
can be reformulated in terms of a probability transport equation, whose moments
determine the correlation properties of the primordial curvature perturbation.
In this paper we generalize this formulation to an arbitrary number of fields.
We deduce ordinary differential equations for the evolution of the moments of
zeta on superhorizon scales, which can be used to obtain an evolution equation
for the dimensionless bispectrum, fNL. Our equations are covariant in field
space and allow identification of the source terms responsible for evolution of
fNL. In a model with M scalar fields, the number of numerical integrations
required to obtain solutions of these equations scales like O(M^3). The
performance of the moment transport algorithm means that numerical calculations
with M >> 1 fields are straightforward. We illustrate this performance with a
numerical calculation of fNL in Nflation models containing M ~ 10^2 fields,
finding agreement with existing analytic calculations. We comment briefly on
extensions of the method beyond the slow-roll approximation, or to calculate
higher order parameters such as gNL.
