One-photon pair production on the expanding de Sitter spacetime

We study the one-photon scalar pair production QED process on the expanding de Sitter spacetime. Using perturbation theory, we obtain the transition probability and study its properties as a function of the expansion parameter $\omega$. On flat space the process is forbidden by energy-momentum conservation. It is expected that for a dynamical background there is an energy exchange correlate to the strength of the gravitational field. We use momentum space plots and compute the mean production angle to illustrate this. We show that the mean angle grows with $\omega$, but also find that in the flat limit the fall-off is unexpectedly slow. To investigate this further we obtain the probability around different angular configuration, at leading order in $m/\omega$, and find that the $\omega$ dependence at small angles is very weak. We comment on the possible astrophysical implications.