  After a brief review of the different approaches to predict the possible
quantum gravity corrections to quantum field theory, we discuss in some detail
the formulation based on a Gaussian reference frame fixing. Then, we implement
this scenario to the determination of the inflationary spectrum of primordial
perturbations. We consider the quantization of an inhomogeneous free massless
scalar field on a quasi-classical isotropic Universe, developing a WKB
expansion of the dynamics at the next order in the Planckian parameter, with
respect to the one at which standard QFT emerges. The quantum gravity
corrections to the scale invariant spectrum are discussed in a specific
primordial cosmological setting and then in a general minisuperspace formalism,
showing that there is no mode-dependent effect and thus the scale invariant
inflationary spectrum is preserved. Such result is discussed in connection to
the absence of a matter backreaction on the gravitational background in the
considered paradigm.
