Stochastic gravity-wave background in inflationary-universe models

The gravitational-wave-noise power spectrum P(ω) is found for a simple cosmological model with an ‘‘inflationary’’ early stage of expansion. The source of the gravitational-wave noise is quantum fluctuations during the inflationary de Sitter stage, which are amplified by the subsequent expansion of the Universe. The resulting spectrum P(ω) is compared to a naive estimate: a thermal spectrum at the (appropriately red-shifted) Gibbons-Hawking temperature. The two spectra are remarkably different. Unlike the thermal spectrum, P(ω) increases at low frequencies. We show that the source of the corresponding long-wavelength perturbations is a global gravitational instability during the inflationary de Sitter stage of expansion. An interesting consequence of the low-frequency behavior of P(ω) is that gravitational radiation contributes a constant fraction of the energy density of the Universe, even after the time of matter domination