There is an extremely simple relationship between the spectrum of the
gravitational wave background produced by a cosmological distribution of
discrete gravitational wave sources, the total time-integrated energy spectrum
of an individual source, and the present-day comoving number density of
remnants. Stated in this way, the background is entirely independent of the
cosmology, and only weakly dependent on the evolutionary history of the
sources. This relationship allows one easily to compute the amplitude and
spectrum of cosmic gravitational wave backgrounds from a broad range of
astrophysical sources, and to evaluate the uncertainties therein.Comment: 7 pages, no figures, uses mn2e.cls; submitted to MNRA
