Non-Particulate Quantum States of the Electromagnetic Field in Expanding Space-Time

TL;DR

This paper investigates the behavior of quantum electromagnetic fields in an expanding universe, revealing how modes become unstable and contribute to cosmic energy, with implications for quantum field theory in curved spacetime.

Contribution

It introduces a detailed analysis of non-particulate quantum states of electromagnetic fields in expanding space-time, including stability properties and the structure of the Hamiltonian.

Findings

Unstable modes increase rapidly, contributing significantly to cosmic energy.

Subsystem Hamiltonian can be unbounded below, lacking a simple number operator representation.

Existence of a vacuum state in a Fock-Cook representation for certain modes.

Abstract

A quantum field has been coupled to a space-time with accelerating expansion. Dynamical modes are destabilised successively at shorter material wavelengths as they metamorphose from oscillators to repellers. Due to degeneracy of energy levels, the number of unstable modes increases at an accelerating rate, sufficient to account for a significant proportion of cosmic energy. For the subsystem spanned by a finite basis of unstable runaway modes, the quantum Hamiltonian is unbounded below. There is no Bogoliubov transformation by which that subsystem Hamiltonian can be expressed as a linear combination of number operators. For the remaining subsystem spanned by an infinite number of oscillator modes, there is an appropriate vacuum state in a Fock-Cook representation of the field algebra. The massless quantum vector field of electromagnetism is considered when it is minimally or more generally coupled to an expanding space-time. For a significant class of models, including minimal coupling models and the exponential de Sitter universe coupled to the Ricci curvature tensor, the field equations are equivalent to the Proca equation with time-dependent mass.