Analyzing the influence of graviton fluctuations on the inflationary spectrum with a Kuchař-Torre clock

This paper focuses on the search for a coherent and consistent formulation to describe quantum gravity corrections to quantum field theory. We implement two fundamental ingredients discussed in previous analyses: on one hand, the construction of the Wentzel-Kramer-Brillouin and Born-Oppenheimer picture for the Wheeler-DeWitt theory of gravity and matter by using a reference fluid as physical clock; on the other hand, we explicitly separate in the metric field its own purely classical contribution from the quantum graviton degrees of freedom. This allows to derive, by the expansion in a Planckian parameter, a unitary theory properly evaluating the quantum field theory modifications in the considered regime. More specifically, we recover at zero order the standard theory on curved space-time after averaging over the graviton sector. The physical corrections are induced at first order by (quantum) gravitons, thought as the slow-varying component of the system, as opposed to the fast quantum matter and reference fluid. The genuine contribution due to gravitons, nonfactorizable into an independent phase, provides a coherent quantum gravity modification on quantum field theory. We show this by determining the predicted inflationary spectrum during an exact de Sitter phase of the primordial Universe, finding a breaking of the scale invariant morphology even when the inflation potential is modeled by a cosmological constant term. Remarkably, the behavior of such non-scale-invariant spectrum overlaps predictions previously obtained in literature by neglecting nonunitary terms emerging in those formulations. In this respect, the present model provides a satisfactory regularization of such approaches by virtue of a more realistic construction of the physical clock for the total (gravity+matter) quantum dynamics.