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One of the crucial windows for distinguishing astrophysical black holes fromprimordial black holes is through the redshift evolution of their respectivemerger rates. The low redshift population of black holes of astrophysicalorigin is expected to follow the star formation rate. The corresponding peak intheir merger rate peaks at a redshift smaller than that of the star formationrate peak ($z_p \approx 2$), depending on the time delay between the formationand mergers of black holes. Black holes of primordial origin are going to bepresent before the formation of the stars, and the merger rate of these sourcesat high redshift is going to be large. We propose a joint estimation of ahybrid merger rate from the stochastic gravitational wave background, which canuse the cosmic history of merger rates to distinguish between the twopopulations of black holes. Using the latest bounds on the amplitude of thestochastic gravitational wave background amplitude from the third observationrun of LIGO/Virgo, we obtain weak constraints at $68\%$ C.L. on the primordialblack hole merger rate index $2.56_{-1.76}^{+1.64}$ and astrophysical blackhole time delay $6.7_{-4.74}^{+4.22}$ Gyr. We should be able to distinguishbetween the different populations of black holes with the forthcoming O5 and A+detector sensitivities.

Can we distinguish astrophysical from primordial black holes via the stochastic gravitational wave background?