Possibility of determining cosmological parameters from measurements of gravitational waves emitted by coalescing, compact binaries

We explore the feasibility of using LIGO and/or VIRGO gravitational-wave measurements of coalescing, neutron-star-neutron-star (NS-NS) binaries and black-hole-neutron-star (BH-NS) binaries at cosmological distances to determine the cosmological parameters of our Universe. From the observed gravitational waveforms one can infer, as direct observables, the luminosity distance D of the source and the binary's two "redshifted masses," M₁^'≡M₁(1+z) and M₂^'≡M₂(1+z), where Mᵢ are the actual masses and z≡Δλλ is the binary's cosmological redshift. Assuming that the NS mass spectrum is sharply peaked about 1.4M_, as binary pulsar and x-ray source observations suggest, the redshift can be estimated as z=MNS^'1.4M_-1. The actual distance-redshift relation $D(z)$ for our Universe is strongly dependent on its cosmological parameters [the Hubble constant H₀, or h₀≡H₀100 km s^-1Mpc^-1, the mean mass density ρₘ, or density parameter Ω₀≡(8π3H₀²)ρₘ, and the cosmological constant Λ, or λ₀≡Λ(3H₀²)], so by a statistical study of (necessarily noisy) measurements of D and z for a large number of binaries, one can deduce the cosmological parameters. The various noise sources that will plague such a cosmological study are discussed and estimated, and the accuracies of the inferred parameters are determined as functions of the detectors' noise characteristics, the number of binaries observed, and the neutron-star mass spectrum. The dominant source of error is the detectors' intrinsic noise, though stochastic gravitational lensing of the waves by intervening matter might significantly influence the inferred cosmological constant λ₀, when the detectors reach "advanced" stages of development. The estimated errors of parameters inferred from BH-NS measurements can be described by the following rough analytic fits: Δh₀h₀0.02(Nh₀)(τR)^-1/2 (for Nh₀2), where N is the detector's noise level (strain√Hz) in units of the "advanced LIGO" noise level, R is the event rate in units of the best-estimate value, 100 yr^-1 Gpc^-3, and τ is the observation time in years. In a "high density" universe (Ω₀=1, λ₀=0), ΔΩ₀0.3(Nh₀)²(τR)^-1/2, Δλ₀0.4(Nh₀)1.5(τR)^-1/2, for Nh₀1. In a "low density" universe (Ω₀=0.2, λ₀=0), ΔΩ₀0.5(Nh₀)³(τR)^-1/2, Δλ₀0.7(Nh₀)2.5(τR)^-1/2, also for Nh₀1. These formulas indicate that, if event rates are those currently estimated ({~}3 per year out to 200 Mpc), then when the planned LIGO and/or VIRGO detectors get to be about as sensitive as the so-called "advanced detector level" (presumably in the early 2000s), interesting cosmological measurements can begin.