  In a class of (pseudoscalar) inflation, inflationary phase is followed by a
kination phase, where the Universe is dominated by the kinetic energy of the
inflaton that runs away in a vanishing scalar potential. In this class of
postinflationary evolution of the Universe, reheating of the Universe cannot be
achieved by the inflaton particle decay, which requires its coherent
oscillation in a quadratic potential. In this study, we explore the U(1) gauge
field production through the Chern-Simons coupling between the pseudoscalar
inflaton and the gauge field during the kination era and examine the subsequent
pair-particle production induced by the amplified gauge field known as the
Schwinger effect, which can lead to reheating of the Universe. We find that
with a rough estimate of the Schwinger effect for the Standard Model hyper U(1)
gauge field and subsequent thermalization of the pair-produced particles, a
successful reheating of the Universe can be achieved by their eventual
domination over the kinetic energy of the inflaton, with some reasonable
parameter sets. This can be understood as a concrete realization of the
"Schwinger reheating". Constraints from the later-time cosmology are also
discussed.
