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

TL;DR

This paper investigates how quantum gravity corrections influence matter dynamics in a cosmological setting, deriving a modified quantum field theory with a physical clock and analyzing the first-order effects on a scalar field in an isotropic universe.

Contribution

It introduces a novel framework combining a Gaussian reference fluid with a Born-Oppenheimer approach to incorporate quantum gravity corrections into matter dynamics.

Findings

Derived a modified quantum field theory with a Hermitian Hamiltonian

Solved the scalar field dynamics up to first-order Planckian corrections

Provided explicit form of the corrected scalar wave-function in cosmology

Abstract

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