Quantum kinetic approach to the Schwinger production of scalar particles in an expanding universe

We study the Schwinger pair creation of scalar charged particles by a homogeneous electric field in an expanding universe in the quantum kinetic approach. We introduce an adiabatic vacuum for the scalar field based on the Wentzel-Kramers-Brillouin solution to the mode equation in conformal time and apply the formalism of Bogolyubov coefficients to derive a system of quantum Vlasov equations for three real kinetic functions. Compared to the analogous system of equations previously reported in the literature, the new one has two advantages. First, its solutions exhibit a faster decrease at large momenta which makes it more suitable for numerical computations. Second, it predicts no particle creation in the case of conformally coupled massless scalar field in the vanishing electric field, i.e., it respects the conformal symmetry of the system. We identify the ultraviolet divergences in the electric current and energy-momentum tensor of produced particles and introduce the corresponding counterterms in order to cancel them.