Measuring a Cosmological Distance-Redshift Relationship Using Only Gravitational Wave Observations of Binary Neutron Star Coalescences

Detection of gravitational waves from the inspiral phase of binary neutron star coalescence will allow us to measure the effects of the tidal coupling in such systems. Tidal effects provide additional contributions to the phase evolution of the gravitational wave signal that break a degeneracy between the system’s mass parameters and redshift and thereby allow the simultaneous measurement of both the effective distance and the redshift for individual sources. Using the population of $\mathcal{O}({10}^3–{10}^7)$ detectable binary neutron star systems predicted for 3rd generation gravitational wave detectors, the luminosity distance-redshift relation can be probed independently of the cosmological distance ladder and independently of electromagnetic observations. We conclude that for a range of representative neutron star equations of state the redshift of such systems can be determined to an accuracy of 8%–40% for $z<1$ and 9%–65% for $1<z<4$.

Figure 1

The fractional uncertainties in the redshift as a function of redshift obtained from the Fisher matrix analysis for BNS systems using 3 representative EOSs: APR [40], SLy [41], and MS1 [42]. In all cases the component NSs have rest masses of $1.4M_{\odot }$ and waveforms have a cutoff frequency equal to the ISCO frequency (as defined in the BNS rest frame). We have used a cosmological parameter set $H_0=70.5\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$, ${\Omega }_m=0.2736$, ${\Omega }_k=0$, $w_0=-1$ to compute the luminosity distance for given redshifts and have assumed detector noise corresponding to the ET-D [16, 39] design (a frequency domain analytic fit to the noise floor can be found in 45).