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 rho and chirp mass M. The distribution of events in a catalog composed of observations with rho greater than a threshold rho(0) 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 rho 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 rho > 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 rho 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.