Impact of O4 future detections on the determination of the dense matter equations of state

In view of the next LIGO-Virgo-KAGRA Observing period O4 (to start in Spring 2023), we address the question of the ability of the interferometers network to discriminate among different neutron stars equation of states better than what was possible with the observation of the binary neutron stars merger GW170817. We show that the observation of an event similar to GW170817 during O4 would allow us to resolve the dimensionless effective tidal deformability Λ ∼ within an uncertainty 7 times better than the one obtained in O2. Thanks to the expected increase in sensitivities, we show that any GW170817-like single-event within a distance of 100 Mpc would imply significantly improved constraints of the neutron stars equations of state. We also illustrate the important impact of the noise in the analysis of the signal, showing how it can impact the effective tidal deformability probability density function for large signal-to-noise ratio.