Gravitational radiation, inspiraling binaries, and cosmology

We show how to measure cosmological parameters using observations of inspiraling binary neutron star or black hole systems in one or more gravitational wave detectors. To illustrate, we focus on the case of fixed mass binary systems observed in a single Laser Interferometer Gravitational-wave Observatory (LIGO)-like detector. Using realistic detector noise estimates, we characterize the rate of detections as a function of a threshold signal-to-noise ratio ρ₀, the Hubble constant H₀, and the binary ``chirp'' mass. For ρ₀ = 8, H₀ = 100 km/s/Mpc, and 1.4 neutron star binaries, the sample has a median redshift of $0.22$. Under the same assumptions but independent of H₀, a conservative rate density of coalescing binaries (8×10⁻⁸\, yr⁻¹\, Mpc⁻³) implies LIGO will observe ~ 50\, yr⁻¹ binary inspiral events. The precision with which H₀ and the deceleration parameter q₀ may be determined depends on the number of observed inspirals. For fixed mass binary systems, ~ 100 observations with ρ₀ = 10 in the LIGO detector will give H₀ to 10% in an Einstein-DeSitter cosmology, and 3000 will give q₀ to 20%. For the conservative rate density of coalescing binaries, 100 detections with ρ₀ = 10 will require about 4~yrs.