Can we distinguish astrophysical from primordial black holes via the
  stochastic gravitational wave background?
  One of the crucial windows for distinguishing astrophysical black holes from
primordial black holes is through the redshift evolution of their respective
merger rates. The low redshift population of black holes of astrophysical
origin is expected to follow the star formation rate. The corresponding peak in
their merger rate peaks at a redshift smaller than that of the star formation
rate peak ($z_p \approx 2$), depending on the time delay between the formation
and mergers of black holes. Black holes of primordial origin are going to be
present before the formation of the stars, and the merger rate of these sources
at high redshift is going to be large. We propose a joint estimation of a
hybrid merger rate from the stochastic gravitational wave background, which can
use the cosmic history of merger rates to distinguish between the two
populations of black holes. Using the latest bounds on the amplitude of the
stochastic gravitational wave background amplitude from the third observation
run of LIGO/Virgo, we obtain weak constraints at $68\%$ C.L. on the primordial
black hole merger rate index $2.56_{-1.76}^{+1.64}$ and astrophysical black
hole time delay $6.7_{-4.74}^{+4.22}$ Gyr. We should be able to distinguish
between the different populations of black holes with the forthcoming O5 and A+
detector sensitivities.
