Classical and quantum radiation from a moving charge in expanding universe

In the present paper, we investigated photon emission from a moving massive charge in an expanding universe. We considered the scalar QED model for simplicity, and focused on the energy radiated by the process. First we showed how the Larmor formula for the radiation energy in the classical electromagnetic theory can be reproduced under the WKB approximation in the framework of the quantum field theory in curved spacetime. We also investigated the limits of the validity of the WKB formula, by deriving the radiation formula in a bouncing universe in which the mode functions are exactly solvable. The result using the exact mode function shows the suppression of the radiation energy compared with the WKB formula. The suppression depends on the ratio of the Compton wavelength λC of the charged particle to Hubble lengthH-1. Namely, the larger the ratio λ_C/H^-1 is, the stronger the suppression becomes. In the limit the Compton wavelength is small compared with the Hubble length, the radiation formula is found to agr e with the WKB formula. Since this limit is equivalent to the limit h → 0, the suppression we found is a genuine quantum effect in an expanding (or contracting) universe, which is due to the finiteness of the Hubble length. Whether the quantum effect on the radiation from a accelerated charge always leads suppression or not is an interesting question. This would be understood by analyzing higher order termsof the WKB approximation.