  A theory of gravitational production of light scalar particles during and
after inflation is investigated. We show that in the most interesting cases
where long-wavelength fluctuations of light scalar fields can be generated
during inflation, these fluctuations rather than quantum fluctuations produced
after inflation give the dominant contribution to particle production. In such
cases a simple analytical theory of particle production can be developed.
Application of our results to the theory of quantum creation of moduli fields
demonstrates that if the moduli mass is smaller than the Hubble constant then
these fields are copiously produced during inflation. This gives rise to the
cosmological moduli problem even if there is no homogeneous component of the
classical moduli field in the universe. To avoid this version of the moduli
problem it is necessary for the Hubble constant H during the last stages of
inflation and/or the reheating temperature T_R after inflation to be extremely
small.
