Gravitational particle production and the moduli problem

A theory of gravitational production of light scalar particles during and a fter 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 produ ced after inflation give the dominant contribution to particle production. In such cases a simple analytical theory of particle production can be deve loped. Application of our results to the theory of quantum creation of modu li fields demonstrates that if the moduli mass is smaller than the Hubble c onstant then these fields are copiously produced during inflation. This giv es rise to the cosmological moduli problem even if there is no homogeneous component of the classical moduli field in the universe. To avoid this vers ion 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 inf lation to be extremely small.