The gravitational wave background from cosmological compact binaries

We use a population synthesis approach to characterize, as a function of cosmic time, the extragalactic close binary population descended from stars of low to intermediate initial mass. The unresolved gravitational wave (GW) background due to these systems is calculated for the 0.1-10 mHz frequency band of the planned Laser Interferometer Space Antenna (LISA). This background is found to be dominated by emission from close white dwarf-white dwarf (WD-WD) pairs. The spectral shape can be understood in terms of some simple analytic arguments. To quantify the astrophysical uncertainties, we construct a range of evolutionary models which produce populations consistent with Galactic observations of close WD-WD binaries. The models differ in binary evolution prescriptions as well as initial parameter distributions and cosmic star formation histories. We compare the resulting background spectra, the shapes of which are found to be insensitive to the model chosen, and different to those found recently by Schneider et al. From this set of models, we constrain the amplitude of the extragalactic background to be 1 x 10(-12)less than or similar to Omega(gw)(1 mHz) less than or similar to 6 x 10(-12), in terms of Omega(gw)(f), the fraction of closure density received in gravitational waves in the logarithmic frequency interval around f.