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 M(i) are the actual masses and z = DELTAlambda/lambda 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(NS)'/1.4M. - 1. The actual distance-redshift relation D(z) for our Universe is strongly dependent on its cosmological parameters [the Hubble constant H-0, or h0 = H-0/100 km s-1 Mpc-1, the mean mass density rho(m), or density parameter OMEGA0 - (8pi/3H02)rho(m), and the cosmological constant LAMBDA, or lambda0 = LAMBDA/(3H0(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 lambda0, 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: DELTAh0/h0 congruent-to 0.02(N/h0)(tauR)-1/2 (for N/h0 less than or similar to 2), where N is the detector's noise level (strain/square-root 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 tau is the observation time in years. In a ''high density'' universe (OMEGA0 = 1, lambda0 = 0) DELTAOMEGA0 congruent-to 0.3(N/h0)2(tauR)-1/2, DELTAlambda0 congruent-to 0.4(N/h0)1.5(tauR)-1/2, for N/h0 less than or similar to 1. In a ''low density'' universe (OMEGA0 = 0.2, lambda0 = 0), DELTAOMEGA0 congruent-to 0.5(N/h0)3(tauR)-1/2, DELTAlambda0 congruent-to 0.7(N/h0)2.5(tauR)-1/2, also for N/h0 less than or similar to 1. These formulas indicate that, if event rates are those currently estimated (approximately 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.