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• W2030255637 abstract "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, ${M}_{1}^{ensuremath{'}}ensuremath{equiv}{M}_{1}(1+z)$ and ${M}_{2}^{ensuremath{'}}ensuremath{equiv}{M}_{2}(1+z)$, where ${M}_{i}$ are the actual masses and $zensuremath{equiv}frac{ensuremath{Delta}ensuremath{lambda}}{ensuremath{lambda}}$ is the binary's cosmological redshift. Assuming that the NS mass spectrum is sharply peaked about $1.4{M}_{ensuremath{bigodot}}$, as binary pulsar and x-ray source observations suggest, the redshift can be estimated as $z=frac{{M}_{mathrm{NS}}^{ensuremath{'}}}{1.4{M}_{ensuremath{bigodot}}}ensuremath{-}1$. The actual distance-redshift relation $D(z)$ for our Universe is strongly dependent on its cosmological parameters [the Hubble constant ${H}_{0}$, or ${h}_{0}ensuremath{equiv}frac{{H}_{0}}{100}$ km ${mathrm{s}}^{ensuremath{-}1}$M${mathrm{pc}}^{ensuremath{-}1}$, the mean mass density ${ensuremath{rho}}_{m}$, or density parameter ${ensuremath{Omega}}_{0}ensuremath{equiv}(frac{8ensuremath{pi}}{3{H}_{0}^{2}}){ensuremath{rho}}_{m}$, and the cosmological constant $ensuremath{Lambda}$, or ${ensuremath{lambda}}_{0}ensuremath{equiv}frac{ensuremath{Lambda}}{(3{H}_{0}^{2})}$], 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 ${ensuremath{lambda}}_{0}$, 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: $frac{ensuremath{Delta}{h}_{0}}{{h}_{0}}ensuremath{simeq}0.02(frac{N}{{h}_{0}}){(ensuremath{tau}mathcal{R})}^{ensuremath{-}frac{1}{2}}$ (for $frac{N}{{h}_{0}}ensuremath{lesssim}2$), where $N$ is the detector's noise level ($frac{mathrm{strain}}{sqrt{mathrm{Hz}}}$) in units of the advanced LIGO noise level, $mathcal{R}$ is the event rate in units of the best-estimate value, 100 ${mathrm{yr}}^{ensuremath{-}1}$ G${mathrm{pc}}^{ensuremath{-}3}$, and $ensuremath{tau}$ is the observation time in years. In a high density universe (${ensuremath{Omega}}_{0}=1$, ${ensuremath{lambda}}_{0}=0$), $ensuremath{Delta}{ensuremath{Omega}}_{0}ensuremath{simeq}0.3{(frac{N}{{h}_{0}})}^{2}{(ensuremath{tau}mathcal{R})}^{ensuremath{-}frac{1}{2}}$, $ensuremath{Delta}{ensuremath{lambda}}_{0}ensuremath{simeq}0.4{(frac{N}{{h}_{0}})}^{1.5}{(ensuremath{tau}mathcal{R})}^{ensuremath{-}frac{1}{2}}$, for $frac{N}{{h}_{0}}ensuremath{lesssim}1$. In a low density universe (${ensuremath{Omega}}_{0}=0.2$, ${ensuremath{lambda}}_{0}=0$), $ensuremath{Delta}{ensuremath{Omega}}_{0}ensuremath{simeq}0.5{(frac{N}{{h}_{0}})}^{3}{(ensuremath{tau}mathcal{R})}^{ensuremath{-}frac{1}{2}}$, $ensuremath{Delta}{ensuremath{lambda}}_{0}ensuremath{simeq}0.7{(frac{N}{{h}_{0}})}^{2.5}{(ensuremath{tau}mathcal{R})}^{ensuremath{-}frac{1}{2}}$, also for $frac{N}{{h}_{0}}ensuremath{lesssim}1$. These formulas indicate that, if event rates are those currently estimated (ensuremath{sim}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." @default.
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• W2030255637 date "1993-11-15" @default.
• W2030255637 modified "2023-09-23" @default.
• W2030255637 title "Possibility of determining cosmological parameters from measurements of gravitational waves emitted by coalescing, compact binaries" @default.
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• W2030255637 doi "https://doi.org/10.1103/physrevd.48.4738" @default.
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