Lorentz Gauge Quantization in a Cosmological Space-time

TL;DR

This paper demonstrates that the Lorentz gauge condition can be imposed in a cosmological space-time using Dirac's quantization method, and shows that the electromagnetic field does not contribute to dark energy.

Contribution

It introduces the use of Dirac's method for Lorentz gauge quantization in cosmology, contrasting with previous approaches that failed in this context.

Findings

Lorentz gauge can be imposed with Dirac's method in cosmological space-time.

Vacuum expectation value of the energy-momentum tensor vanishes.

Electromagnetic field does not contribute to dark energy in this framework.

Abstract

It has recently been shown that it is not possible to impose the Lorentz gauge condition in a cosmological space-time using the Gutpa-Bleuler method of quantization. It was also shown that it is possible to add $\nabla_{\mu}A^{\mu}$ as a new degree of freedom to the electromagnetic field and that this new degree of freedom might be the dark energy which is producing the accelerated expansion of the Universe. In this paper I show that the Lorentz gauge condition can be imposed using Dirac's method of quantizing constrained dynamical systems. I also compute the vacuum expectation value of the energy-momentum tensor and show that it vanishes. Thus, in Dirac's approach, the electromagnetic field does not make a contribution to the dark energy.