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 M₈ are the actual masses and z 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=M₍ₒ^{'}1. 4{M_}-1. The actual distance-redshift relation D (z) for our Universe is strongly dependent on its cosmological parameters the Hubble constant H₀, or h₀H₀100 km s^-1Mpc^-1, the mean mass density ₌, or density parameter ₀ (83{H₀^2}) ₌, and the cosmological constant, or ₀ (3{H₀^2) }, 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 ₀, 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: {h₀}{h₀}0. 02 (N{h₀}) () ^-1{2} (for N{h₀}2), where N is the detector's noise level (strainHz) 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 is the observation time in years. In a "high density" universe (₀=1, ₀=0), ₀0. 3 (N{{h₀}) }^2 () ^-1{2}, ₀0. 4 (N{{h₀}) }^1. 5 () ^-1{2}, for N{h₀}1. In a "low density" universe (₀=0. 2, ₀=0), ₀0. 5 (N{{h₀}) }^3 () ^-1{2}, ₀0. 7 (N{{h₀}) }^2. 5 () ^-1{2}, also for N{h₀}1. 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.