We compute the covariant three-point function near horizon-crossing for a
system of slowly-rolling scalar fields during an inflationary epoch, allowing
for an arbitrary field-space metric. We show explicitly how to compute its
subsequent evolution using a covariantized version of the separate universe or
"delta-N" expansion, which must be augmented by terms measuring curvature of
the field-space manifold, and give the nonlinear gauge transformation to the
comoving curvature perturbation. Nonlinearities induced by the field-space
curvature terms are a new and potentially significant source of
non-Gaussianity. We show how inflationary models with non-minimal coupling to
the spacetime Ricci scalar can be accommodated within this framework. This
yields a simple toolkit allowing the bispectrum to be computed in models with
non-negligible field-space curvature.Comment: 22 pages, plus appendix and reference
