Effect of Distance-Inclination Angle Degeneracy on Hubble-Lemaitr\'e Constant Measurement

The discovery of GW170817 and its electromagnetic counterparts allowed the first independent measurement of Hubble-Lamaitr\'e constant ($H_0$) using gravitational waves (GWs). Such $H_0$ measurement, in the local universe, requires the correct estimation of the binary's distance from its GW signal and the redshift information of the host galaxy from optical observations. Though the measurement of host's redshift, if identified correctly, can be very accurate (within $\sim1\%$ error), the distance estimates through GWs suffer from large uncertainties mainly due to distance-inclination angle ($D_L-\iota$) degeneracy, hence, affecting the $H_0$ measurements. In this presentation, we exploit this degeneracy to constrain $H_0$ effectively. The distance posterior is asymmetric due to $D_L-\iota$ degeneracy and leads to an asymmeteric joint $H_0$ posterior for a population of binary neutron star (BNS) mergers. This results in uneven credible intervals measured from the maximum likelihood estimator of the $H_0$ posterior, left error bar being smaller than the right error bar. Using this feature of joint $H_0$ posterior, we show that the advanced LIGO-Virgo detector network will need only $\sim30$ BNS mergers (with counterparts) to rule-out Plank Collaboration's $H_0$ estimate.