Influence of cosmic expansion on gravitational waveforms

TL;DR

This paper explores how cosmic expansion affects gravitational waveforms, demonstrating that certain dimensionless parameters can break the redshift-mass degeneracy and enabling redshift measurement from postmerger signals with upcoming detectors.

Contribution

It introduces a method to break the redshift-mass degeneracy in gravitational wave observations using dimensionless parameters from postmerger signals and provides a corrected phase correction derivation.

Findings

Redshift can be measured with ~30% uncertainty for sources at z=0.01-0.09.

Dimensionless parameters like quality factors and frequency ratios help break degeneracy.

Corrected the waveform phase correction derivation related to redshift drift.

Abstract

Gravitational waves undergo redshift as they propagate through the expanding universe, and the redshift may exhibit time-dependent drift. Consequently, for any isolated gravitational wave sources, the mass parameter $\mathcal{M}$ and the redshift $z$ exhibit an observational degeneracy, typically manifesting in the waveform as the redshifted mass $\mathcal{M}(1+z)$. Matching together the wave propagation and the wave generation solutions, we show that dimensionless source parameters depending on mass $\mathcal{M}$ can break this degeneracy. Notably, the postmerger signal from binary neutron stars contains several dimensionless parameters that satisfy this condition, including the quality factors of different frequency components and their frequency ratios. Considering the observations of solely the postmerger signal by the Neutron star Extreme Matter Observatory or the Einstein Telescope, based on the Fisher analysis, we find that the redshift can be measured with fractional uncertainties of $\sim30\%$ for sources at $0.01<z<0.09$. Additionally, we present a corrected derivation of the waveform phase correction due to the redshift drift effect, rectifying a sign error in previous studies.