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We present an extension of the semiclassical Einstein equations which couplesn-point correlation functions of a stochastic Einstein tensor to the n-pointfunctions of the quantum stress-energy tensor. We apply this extension tocalculate the quantum fluctuations during an inflationary period, where we takeas a model a massive conformally coupled scalar field on a perturbed de Sitterspace and describe how a renormalization independent, almost-scale-invariantpower spectrum of the scalar metric perturbation is produced. Furthermore, wediscuss how this model yields a natural basis for the calculation ofnon-Gaussianities of the considered metric fluctuations.

Scale-Invariant Curvature Fluctuations from an Extended Semiclassical Gravity