Formation of primordial black hole binaries and their merger rates

We review the theory behind the formation of primordial black hole binaries and their merger rates. We consider the binary formation in the early and late Universe, emphasising the former as it gives the dominant contribution of the present primordial black hole merger rate. The binaries formed in the early Universe are highly eccentric so their interactions with other primordial black holes can significantly increase their coalescence times and thereby suppress the merger rate. We discuss in detail how the suppression of the merger rate arising from such interactions can be estimated and how such interactions lead to the formation of another, much harder, binary population that contributes to the present merger rate if more than 10% of dark matter consists of primordial black holes with a relatively narrow mass distribution. When the primordial abundance is below 1%, encounters between primordial black holes are unlikely and their effect on the merger rate becomes negligible.