Evolution of the merger rate density in the comoving frame as a function of redshift for the BNS populations used in the present work. Our fiducial population is obtained with a common envelope efficiency α_CE = 3 and is represented by the orange solid line. The pessimistic and optimistic populations are obtained with α_CE = 0.5 and 5 and are shown by blue and green solid lines, respectively. The grey area shows the 90% credible interval of the local merger rate density, as inferred from the first three observing runs of LIGO, Virgo, and KAGRA (Abbott et al. 2023).