Mathematics – Logic
Scientific paper
Jul 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993phrvd..48..647d&link_type=abstract
Physical Review D, Vol. 48, No. 2, p. 647 - 662
Mathematics
Logic
24
Early Universe: Gravitational Radiation, Cosmological Models: Gravitational Radiation
Scientific paper
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 to 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 Ωg are found. From considerations involving the production of primordial 4He it is shown how the maximum allowed value for Ωg 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.
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