Scale-Invariant Curvature Fluctuations from an Extended Semiclassical
  Gravity
  We present an extension of the semiclassical Einstein equations which couples
n-point correlation functions of a stochastic Einstein tensor to the n-point
functions of the quantum stress-energy tensor. We apply this extension to
calculate the quantum fluctuations during an inflationary period, where we take
as a model a massive conformally coupled scalar field on a perturbed de Sitter
space and describe how a renormalization independent, almost-scale-invariant
power spectrum of the scalar metric perturbation is produced. Furthermore, we
discuss how this model yields a natural basis for the calculation of
non-Gaussianities of the considered metric fluctuations.
