  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.
