COSMOLOGICAL GRAVITON PRODUCTION IN GENERAL-RELATIVITY AND RELATED GRAVITY THEORIES

A unified description of graviton creation is given for isotropic cosmological models in general relativity, Brans-Dicke theory, and higher-order gravity theories. The Bogolubov coefficents are derived in general and may be specialized to each of the possible gravity theories. The power spectrum and energy density of relic gravitons surviving a variety of early cosmological scenarios are calculated. The possibility of a nonvacuum initial state is allowed for and the problems of imposing an ultraviolet cutoff are analyzed. We distinguish carefully the effects of gravity waves on super- and subhorizon scales. The associated infrared cutoff, or the Allen effect, is discussed in detail in order to evaluate the dependence of the graviton energy density on the expansion scale factor. It is found that the nonadiabatic evolution of the graviton energy density can occur even during the radiation era when long-wavelength primoridal gravitational waves enter the horizon. Detailed, multistage, cosmological models are set up involving a sequence of changes in the equation of state for general relativity and Brans-Dicke theories. These examples include models with an inflationary phase. The resulting gravitational-wave background is calculated analytically over the whole frequency range in all cases. The limits imposed by nucleosynthesis of helium-4 are found for general relativity. We also investigate the effects of the presence of a thermal sea of gravitons in the initial state prior to gravitational-wave amplification by the expansion and calculate the effects of the small horizon size upon the thermal distributions. © 1994 The American Physical Society.