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 Rₘₑᵣ ~ 100 (300) Gpc⁻³ yr⁻¹ at z~ 0(2), we can reconstruct the merger rate density uptil z ~ 2 , with a relative error of $12%$ at (z ~ 2), despite the loss in detection of the bulk of the BNS population.