Schwinger Effect in a Robertson-Walker Space-Time

The problem of particle creation from vacuum in a flat Robertson-Walker space-time in the presence of a varying electric field is studied. The Klein Gordon equation is exactly solved when the scale factor is a(η)=A+Btanh(λη). The canonical method based on Bogoliubov transformation is applied. The pair creation probability and the density number of created particles are calculated. The particular case of radiation dominated universe is considered where the total probability is written as a Schwinger-like series. It is shown that the electric field amplifies gravitational particle creation.