Description
Primordial black holes (PBHs) serve as an interesting probe of the early
Universe and cosmic evolution. In this study, we explore the formation of PBHs
near the QCD phase transition, driven by a broadly peaked inflationary scalar
power spectrum. This mechanism naturally results in an extended PBH mass
distribution and generates two distinct stochastic gravitational-wave backgrounds
(SGWBs): a scalar-induced SGWB from second-order tensor perturbations at the
time of PBH formation, and a merger-driven SGWB arising from the evolution of
the PBH binary population. We analyze both SGWB components using Bayesian
methods, incorporating data from the NANOGrav 15-year dataset and the first
three observing runs of LVK. We also project the continuous-wave signals
expected from mini extreme–mass-ratio inspirals (mini-EMRIs), enabling direct
comparison with existing constraints from NANOGrav and LVK. Our
parameter-space analysis reveals regions where the combined SGWB signal may
be detectable by future ground- and space-based gravitational-wave
observatories. Notably, the extended PBH mass spectrum naturally leads to the
formation of mini-EMRIs, which are promising targets for next-generation
ground-based detectors such as upgraded versions of LVK, ET, and CE. In much
of the parameter space, the astrophysical SGWB masks the primordial contribution
in the frequency range accessible to ground-based detectors. As a result, in
scenarios with extended PBH mass functions, the detection of mini-EMRIs
provides a more reliable probe of the PBH landscape than SGWB measurements
alone.
