SPECTRUM AND ENERGY DENSITY OF RELIC GRAVITONS IN FLAT ROBERTSON-WALKER UNIVERSES

Graviton production in flat three-space Robertson-Walker universes is studied. An arbitrary sequence of stages governed by scale factors exhibiting exponential or power-law behavior is considered. By the derivation of exact expressions for the Bogolubov coefficients associated with the several transitions between different cosmic eras, a general method to obtain the power spectrum and energy density of the relic gravitational waves is described. The results are applied for a simple three-stage model involving both an inflationary and noninflationary initial phase. Exact and explicit formulas for the spectrum and time evolution of the energy density parameter OMEGA(g) are found. From considerations involving the production of primordial He-4 it is shown how the maximum allowed value for OMEGA(g) relates to the baryon to photon ratio, the neutron mean life, and the number of light neutrinos. It is found that the energy density associated with the relic gravitons cannot exceed 6% of that associated with photons at the time of nucleosynthesis. From this limit, constraints on some parameters of the early Universe are derived. Independent constraints are obtained by assuming that gravitons do not dominate the cosmic dynamics to day.