  We treat quantum creation of gravitons by small scale factor oscillations
around the average of an expanding universe. Such oscillations can arise in
standard general relativity due to oscillations of a homogeneous, minimally
coupled scalar field. They can also arise in modified gravity theories with a
term proportional to the square of the Ricci scalar in the gravitational
action. The graviton wave equation is different in the two cases, leading to
somewhat different creation rates. Both cases are treated using a perturbative
method due to Birrell and Davies, involving an expansion in a conformal
coupling parameter to calculate the number density and energy density of the
created gravitons. Cosmological constraints on the present graviton energy
density and the dimensionless amplitude of the oscillations are discussed. We
also discuss decoherence of quantum systems produced by the spacetime geometry
fluctuations due to such a graviton bath.
