Quantum field theory on a cosmological, quantum space-time

TL;DR

This paper develops a quantum theory of test scalar fields on quantum geometries derived from loop quantum cosmology, highlighting new conceptual frameworks like relational time and quantum fluctuations.

Contribution

It introduces a framework for quantum field theory on quantum space-times, extending classical FLRW models to incorporate quantum geometric effects.

Findings

Quantum scalar fields can be formulated on quantum FLRW geometries.

Emergence of the Hamiltonian operator from quantum constraints.

Quantum fluctuations influence the dynamics of test fields.

Abstract

In loop quantum cosmology, Friedmann-LeMaitre-Robertson-Walker (FLRW) space-times arise as well-defined approximations to specific \emph{quantum} geometries. We initiate the development of a quantum theory of test scalar fields on these quantum geometries. Emphasis is on the new conceptual ingredients required in the transition from classical space-time backgrounds to quantum space-times. These include a `relational time' a la Leibnitz, the emergence of the Hamiltonian operator of the test field from the quantum constraint equation, and ramifications of the quantum fluctuations of the background geometry on the resulting dynamics. The familiar quantum field theory on classical FLRW models arises as a well-defined reduction of this more fundamental theory.