Imprints of the redshift evolution of double neutron star merger rate on the signal-to-noise ratio distribution

Proposed third-generation gravitational wave interferometers such as Cosmic Explorer (CE) will have the sensitivity to observe double neutron star mergers (DNS) up to a redshift of similar to 5 with good signal-to-noise ratios (SNRs). We argue that the comoving spatial distribution of DNS mergers leaves a unique imprint on the statistical distribution of SNRs of the detected DNS mergers. Hence, the SNR distribution of DNS mergers will facilitate a novel probe of their redshift evolution independent of the luminosity distance measurements. We consider detections of DNS mergers by the CE and study the SNR distribution for different possible redshift evolution models of DNSs and employ Anderson Darling p value statistic to demonstrate the distinguishability between these different models. We find that a few hundreds of DNS mergers in the CE era will allow us to distinguish between different models of redshift evolution. We further apply the method for various SNR distributions arising due to different merger delay-time and star formation rate (SFR) models and show that for a given SFR model, the SNR distributions are sensitive to the delay-time distributions. Finally, we investigate the effects of sub-threshold events in distinguishing between different merger rate distribution models.