Measuring a cosmological distance-redshift relationship using only gravitational wave observations of binary neutron star coalescences

TL;DR

This paper demonstrates that third-generation gravitational wave detectors can measure the distance-redshift relationship using binary neutron star mergers, independently of electromagnetic observations, by analyzing tidal effects in gravitational wave signals.

Contribution

It introduces a method to determine redshift and distance from gravitational wave data alone, utilizing tidal effects to break degeneracies, and applies Fisher analysis to predict measurement accuracy.

Findings

Redshift can be measured with 8-40% accuracy for z<1.

Redshift can be measured with 9-65% accuracy for 1<z<4.

The method is feasible with the Einstein Telescope for large neutron star populations.

Abstract

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. These effects will be measurable using 3rd generation gravitational wave detectors, e.g. the Einstein Telescope, which will be capable of detecting inspiralling binary neutron star systems out to redshift z=4. 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 O(10^3-10^7) detectable binary neutron star systems predicted for the Einstein Telescope the luminosity distance--redshift relation can be probed independently of the cosmological distance ladder and independently of electromagnetic observations. We present the results of a Fisher information analysis applied to waveforms assuming a subset of possible neutron star equations of state. We conclude that for our 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.