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-wa ve measurements of coalescing, neutron-star-neutron-star (NS-NS) binar ies and black-hole-neutron-star (BH-NS) binaries at cosmological dista nces to determine the cosmological parameters of our Universe. From th e observed gravitational waveforms one can infer, as direct observable s, the luminosity distance D of the source and the binary's two ''reds hifted 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 cosmolog ical redshift. Assuming that the NS mass spectrum is sharply peaked ab out 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 distanc e-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) mea surements of D and z for a large number of binaries, one can deduce th e cosmological parameters. The various noise sources that will plague such a cosmological study are discussed and estimated, and the accurac ies of the inferred parameters are determined as functions of the dete ctors' noise characteristics, the number of binaries observed, and the neutron-star mass spectrum. The dominant source of error is the detec tors' 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 fro m 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/squar e-root Hz) in units of the ''advanced LIGO'' noise level, R is the eve nt 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 (OMEG A0 = 1, lambda0 = 0) DELTAOMEGA0 congruent-to 0.3(N/h0)2(tauR)-1/2, DE LTAlambda0 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 congrue nt-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 esti mated (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-ca lled ''advanced detector level'' (presumably in the early 2000s), inte resting cosmological measurements can begin.