Recovering cosmological parameters from the mock gravitational wave data of the Einstein Telescope

Einstein Telescope (ET) is a third-generation gravitational wave (GW) detector with tenfold better sensitivity compared to the advanced LIGO detectors. It will be capable of observing copious stellar mass binary black hole mergers up to a redshift of 10 which will make it especially useful for cosmography. We generate a mock gravitational wave event catalog for the Einstein Telescope and show the recoverability of either the Hubble constant ($H_0$) or the matter density parameter ($\Omega_{\rm m}$). We present a simple, effective and fast technique for inferring $H_0$ (or $\Omega_{\rm m}$) using the intrinsic chirp mass spectrum of black hole binaries, and investigate the efficacy of the method assuming the standard model of cosmology. If only $H_0$ has to be constrained, we find that at least one year of ET's observation will be required to achieve 1% uncertainty. With the same amount of observation, $\Omega_{\rm m}$ can be constrained to within 4% uncertainty. With ET operating as a standalone instrument, we show that the GW spectral sirens detected by it can constrain the Hubble constant.