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The mass distribution of Primordial Black Holes (PBHs) is affected by dropsin the pressure of the early Universe plasma. For example, events in thestandard model of particle physics, such as the $W^\pm/Z^0$ decoupling, thequark-hadron transition, the muon and pion becoming non-relativistic, and theannihilation of electrons and positrons, cause a suppression in the Equation ofState parameter and leave peaks in the PBH mass function around$10^{-6},\,2,\,60$, and $10^6\, M_\odot$, respectively, in the case of a nearlyscale-invariant primordial power spectrum. The superposition of unresolvedmergers of such PBHs results in a stochastic gravitational-wave background(SGWB) that covers a wide range of frequencies and can be tested with futuregravitational wave (GW) detectors. In this paper, we discuss how its spectralshape can be used to infer properties about inflation, the thermal history ofthe Universe, and the dynamics of binary formation in dense halos encoded intheir merger rate formula. Although many of these physical effects aredegenerate within the sensitivity of a single detector, they can bedisentangled by the simultaneous observation of the SGWB at differentfrequencies, highlighting the importance of multi-frequency observations of GWsto characterize the physics of PBHs from the early to the late time Universe.

Testing Primordial Black Holes with multi-band observations of the stochastic gravitational wave background