Quantum theory of electromagnetic fields in a cosmological quantum spacetime

TL;DR

This paper extends the quantum field theory in cosmological quantum spacetimes to electromagnetic fields, revealing mode-dependent geometries that could influence quantum particle creation in the early universe.

Contribution

It generalizes previous scalar field results to electromagnetic fields, showing how mode-dependent effective geometries emerge in quantum cosmology.

Findings

Mode-dependent (rainbow) metrics arise when backreaction is significant.

Quantum particle production differs on dressed quantum geometries versus classical backgrounds.

Effective geometries are independent of polarization but depend on mode energy.

Abstract

The theory of quantum fields propagating on an isotropic cosmological quantum spacetime is reexamined by generalizing the scalar test field to an electromagnetic (EM) vector field. For any given polarization of the EM field on the classical background, the Hamiltonian can be written in the form of the Hamiltonian of a set of decoupled harmonic oscillators, each corresponding to a single mode of the field. In transition from the classical to quantum spacetime background, following the technical procedure given by Ashtekar {\em et al.} [Phys. Rev. D 79, 064030 (2009)], a quantum theory of the test EM field on an effective (dressed) spacetime emerges. The nature of this emerging dressed geometry is independent of the chosen polarization, but it may depend on the energy of the corresponding field mode. Specifically, when the backreaction of the field on the quantum geometry is negligible (i.e., a test field approximation is assumed), all field modes probe the same effective background independent of the mode's energy. However, when the backreaction of the field modes on the quantum geometry is significant, by employing a Born-Oppenheimer approximation, it is shown that a rainbow (i.e., a mode-dependent) metric emerges. The emergence of this mode-dependent background in the Planck regime may have a significant effect on the creation of quantum particles. The production amount on the dressed background is computed and is compared with the familiar results on the classical geometry.