fNL - gNL mixing in the matter density field at higher orders
  In this paper we examine how primordial non-Gaussianity contributes to
nonlinear perturbative orders in the expansion of the density field at large
scales in the matter dominated era. General Relativity is an intrinsically
nonlinear theory, establishing a nonlinear relation between the metric and the
density field. Representing the metric perturbations with the curvature
perturbation zeta, it is known that nonlinearity produces effective
non-Gaussian terms in the nonlinear perturbations of the matter density field,
even if the primordial zeta is Gaussian. Here we generalise these results to
the case of a non-Gaussian primordial zeta. Using a standard parametrization of
primordial non-Gaussianity in zeta in terms of fNL, gNL, hNL..., we show how at
higher order (from third and higher) nonlinearity also produces a mixing of
these contributions to the density field at large scales, e.g. both fNL and gNL
contribute to the third order in the density contrast. This is the main result
of this paper. Our analysis is based on the synergy between a gradient
expansion (aka long-wavelength approximation) and standard perturbation theory
at higher order. In essence, mathematically the equations for the gradient
expansion are equivalent to those of first order perturbation theory, thus
first-order results convert into gradient expansion results and, vice versa,
the gradient expansion can be used to derive results in perturbation theory at
higher order and large scales.
