Quantum Larmor radiation in a conformally flat universe

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. 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 scalar quantum electrodynamics. 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 ℏ is determined by a nonlocal integration in time depending on the background expansion. We also compare our result with a recent work by Higuchi and Walker [Phys. Rev. D 80, 105019 (2009)], which investigated the quantum correction to the Larmor radiation from a charged particle in a nonrelativistic motion in a homogeneous electric field.

Quantum Larmor radiation in de Sitter spacetime

“…A negative quantum correction was also reported in all similar studies [2][3][4][5][6], for charges evolving in external electromagnetic and gravitational fields. The fact that the quantum effect suppresses the classical result thus seems to be a generic feature in such contexts.…”

“…[6] it is found that the first correction to the radiation of a charge moving in a conformally flat background contains third derivative terms. Up to the orders that we have considered in our case we have ... x (η) 0.…”

“…In Refs. [3,5,6] it is noted that the quantum corrections arise due to a non-local integration in time over the classical trajectory. In our case the trajectory is fixed, with constant accelerationẍ(η) = pω m and the nonlocality is implicit in the result.…”

“…The problem was tackled in Refs. [5,6], in the general case of a conformally flat spacetime, by using the WKB approximation for the mode functions. The authors found that the leading term reproduces exactly the relativistic version of (1), when the trajectory is expressed in terms of conformal time.…”

Quantum radiation from an inertial scalar charge evolving in the de Sitter universe: Weak-field limit

“…Most strikingly, an inertial charge in a dynamic spacetime, which can be thought of as a free charge in an external gravitation field, radiates like an accelerated charge in flat spacetime. This was shown explicitly for the radiation in the WKB approximation for a general conformally flat spacetime, and also for the full quantum radiation in different expanding spacetimes [4,5].…”