  We study production of light particles due to oscillation of the Hubble
parameter or the scale factor. Any coherently oscillating scalar field,
irrespective of its energy fraction in the universe, imprints such an
oscillating feature on them. Not only the Einstein gravity but extended gravity
models, such as models with non-minimal (derivative) coupling to gravity and
$f(R)$ gravity, lead to oscillation of the scale factor. We present a
convenient way to estimate the gravitational particle production rate in these
circumstances. Cosmological implications of gravitational particle production,
such as dark matter/radiation and moduli problem, are discussed. For example,
if the theory is described solely by the standard model plus the Peccei-Quinn
sector, the Starobinsky $R^2$ inflation may lead to observable amount of axion
dark radiation.
