Merger rate density as a function of redshift, for the natal-kick models GM20 (solid lines) and H05 (dashed lines). The line colors show the results obtained assuming different CE efficiency parameters (α). The upper boundaries of the shaded areas show the models obtained with minimum galaxy mass M_* = 10⁶ M_⊙, whereas for the lower boundary the minimum mass is 10⁸ M_⊙. All the models assume the fiducial observational scaling relations. The gray-shaded region shows the MRD inferred by the LVK collaboration (Abbott et al. 2023b).