Gravitational Particle Production and the Moduli Problem

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.