Redshift evolution of primordial black hole merger rate

Abstract: The gravitational wave signals detected by the LIGO-Virgo-KAGRA collaboration can be explained by mergers of binary primordial black holes (PBHs) formed in the radiation dominated epoch. However, in early structures induced by the Poisson distribution of PBHs, a significant fraction of binaries are perturbed and avoid mergers. In addition, the internal dynamics of early halos lead to the formation of dense primordial black hole clusters within a few Hubble times from the moment of halo formation. In such clusters PBH binaries are effectively formed and their mergers potentially dominate in the modern era. We obtained that the PBH merger rate changes with redshift as $\mathcal{R} \propto (1 + z)^\beta$, where $\beta = 1.4 - 2.2$ reflects the influence of PBH clustering and depends on both $z$ and $f_{\rm PBH}$. The observed merger rate constraints the fraction of PBHs of tens solar masses in the composition of dark matter $f_{\rm PBH} \lesssim 0.001 - 0.1$ in dependence of the clustering efficiency.