Estimating the binary neutron star merger rate density evolution with Einstein Telescope

The Einstein Telescope (ET) is a proposed third-generation, wide-band gravitational wave (GW) detector which will have an improved detection sensitivity in low frequencies, leading to a longer observation time in the detection band and higher detection rate for binary neutron stars (BNSs). Despite the fact that ET will have a higher detection rate, a large fraction of BNSs will remain undetectable. We present a scheme to estimate accurate detection efficiency and to reconstruct the true merger rate density of the population of the BNSs, as a function of redshift. We show that with ET as a single instrumnet, for a population of BNSs with $R_{mer} \sim 100 (300)$ $\rm Gpc^{-3} yr^{-1}$ at $z\sim 0(2)$, we can reconstruct the merger rate density uptil $z \sim 2$ , with a relative error of $12\%$ at ($z \sim 2$), despite the loss in detection of the bulk of the BNS population.