  We have studied the merger rate of primordial black holes (PBHs) in the
ellipsoidal-collapse model of halo to explain the dark matter abundance by the
PBH merger estimated from the gravitational waves detections via the Advanced
LIGO (aLIGO) detectors. We have indicated that the PBH merger rate within each
halo for the ellipsoidal models is more significant than for the spherical
models. We have specified that the PBH merger rate per unit time and per unit
volume for the ellipsoidal-collapse halo models is about one order of magnitude
higher than the corresponding spherical models. Moreover, we have calculated
the evolution of the PBH total merger rate as a function of redshift. The
results indicate that the evolution for the ellipsoidal halo models is more
sensitive than spherical halo models, as expected from the models. Finally, we
have presented a constraint on the PBH abundance within the context of
ellipsoidal and spherical models. By comparing the results with the aLIGO
mergers during the third observing run (O3), we have shown that the merger rate
in the ellipsoidal-collapse halo models falls within the aLIGO window, while
the same result is not valid for the spherical-collapse ones. Furthermore, we
have compared the total merger rate of PBHs in terms of their fraction in the
ellipsoidal-collapse halo models for several masses of PBHs. The results
suggest that the total merger rate of PBHs changes inversely with their masses.
We have also estimated the relation between the fraction of PBHs and their
masses in the ellipsoidal-collapse halo model and have shown it for a narrow
mass distribution of PBHs. The outcome shows that the constraint inferred from
the PBH merger rate for the ellipsoidal-collapse halo models can be potentially
stronger than the corresponding result obtained for the spherical-collapse
ones.
