Binary inspiral, gravitational radiation, and cosmology

Observations of binary inspiral in a single interferometric gravitational wave detector can be cataloged according to signal-to-noise ratio ρ and chirp mass M. The distribution of events in a catalog composed of observations with ρ greater than a threshold ρ₀ depends on the Hubble expansion, deceleration parameter, and cosmological constant, as well as the distribution of component masses in binary systems and evolutionary effects. In this paper I find general expressions, valid in any homogeneous and isotropic cosmological model, for the distribution with ρ and M of cataloged events; I also evaluate these distributions explicitly for relevant matter-dominated Friedmann-Robertson-Walker models and simple models of the neutron star mass distribution. In matter-dominated Friedmann-Robertson-Walker cosmological models advanced LIGO detectors will observe binary neutron star inspiral events with ρ>8 from distances not exceeding approximately 2 Gpc, corresponding to redshifts of 0.48 (0.26) for h=0.8(0.5), at an estimated rate of 1 per week. As the binary system mass increases so does the distance it can be seen, up to a limit: in a matter-dominated Einstein-de Sitter cosmological model with h=0.8(0.5) that limit is approximately z=2.7(1.7) for binaries consisting of two 10M_⊙ black holes. Cosmological tests based on catalogs of the kind discussed here depend on the distribution of cataloged events with ρ and M. The distributions found here will play a pivotal role in testing cosmological models against our own universe and in constructing templates for the detection of cosmological inspiraling binary neutron stars and black holes.