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We analyze the effect induced on standard quantum field theory (in functionalapproach) by quantum gravity corrections to a pure classical background. In theframework of the Kucha\v{r} and Torre proposal for a gravity-matter theoryconstrained to a Gaussian reference frame, materialized as a fluid in thesystem evolution, we consider a Born-Oppenheimer separation of the system,regarding the gravity degrees of freedom as the slow varying component and thematter plus the Gaussian fluid as fast quantum coordinates. The slow gravitycomponent obeys the Wheeler-DeWitt equation and we consider aWentzel-Kramer-Brillouin expansion of its quantum dynamics via a Planckianparameter. The main issue of the proposed scenario is that, on one hand, werecover a modified quantum field theory in the presence of an HermitianHamiltonian (not affected by non-unitarity as in other approaches) and, on theother hand, we get the Gaussian fluid as a physical clock for such amendedquantum theory (verifying the correct energy conditions). We also show itsequivalence with the kinematical action method, used in a previous work, in thehomogeneous setting. Then, we implement the proposed paradigm to describe thedynamics of a homogeneous free massless scalar field, living on an isotropicUniverse, in the presence of a cosmological constant. We completely solve thedynamics up to the first order correction in the Planckian parameter to thestandard quantum field theory. We determine the explicit form of the modifiedscalar field wave-function, due to quantum features of the cosmic scale factorevolution. Phenomenological considerations and discussions are provided.

Quantum gravity corrections to the matter dynamics in the presence of a reference fluid