Analyzing the influence of graviton fluctuations on the inflationary spectrum with a Kucha\v{r}-Torre clock

TL;DR

This paper develops a quantum gravity framework incorporating graviton fluctuations as a physical clock, revealing their impact on the inflationary spectrum and showing a deviation from scale invariance during de Sitter inflation.

Contribution

It introduces a unitary quantum gravity correction method using a reference fluid clock, explicitly separating classical and quantum gravitational effects, and applies this to inflationary spectrum analysis.

Findings

Quantum graviton effects induce non-scale-invariant inflationary spectra.

The model regularizes previous non-unitary approaches.

Predictions align with earlier results when neglecting non-unitary terms.

Abstract

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, non-factorizable 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 modelled by a cosmological constant term. Remarkably, the behavior of such non-scale-invariant spectrum overlaps predictions previously obtained in literature by neglecting non-unitary 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.