Quantum Larmor radiation in conformally flat universe

TL;DR

This paper derives a quantum correction formula for Larmor radiation emitted by a moving charge in an expanding universe, analyzing the effects of background expansion on quantum radiation using scalar QED.

Contribution

It provides an analytic evaluation of quantum effects on Larmor radiation in a conformally flat universe, comparing exact solutions with WKB approximation methods.

Findings

Quantum correction depends on non-local time integration and background expansion.

Exact solutions in Milne universe match WKB approximation under certain conditions.

Quantum effects on radiation are of order e^2ħ and influenced by universe expansion.

Abstract

We investigate the quantum effect on the Larmor radiation from a moving charge in an expanding universe based on the framework of the scalar quantum electrodynamics (SQED). A theoretical formula for the radiation energy is derived at the lowest order of the perturbation theory with respect to the coupling constant of the SQED. We evaluate the radiation energy on the background universe so that the Minkowski spacetime transits to the Milne universe, in which the equation of motion for the mode function of the free complex scalar field can be exactly solved in an analytic way. Then, the result is compared with the WKB approach, in which the equation of motion of the mode function is constructed with the WKB approximation which is valid as long as the Compton wavelength is shorter than the Hubble horizon length. This demonstrates that the quantum effect on the Larmor radiation of the order e^2\hbar is determined by a non-local integration in time depending on the background expansion. We also compare our result with a recent work by Higuchi and Walker [Phys. Rev. D80 105019 (2009)], which investigated the quantum correction to the Larmor radiation from a charged particle in a non-relativistic motion in a homogeneous electric field.