Explaining PTA Data with Inflationary GWs in a PBH-Dominated Universe

We show that an ultralight primordial black hole (PBH) dominated phase makes blue-tilted inflationary gravitational waves (BGW) compatible with the recent detection of an nHz stochastic GW background by pulsar-timing arrays (PTAs), for high reheating temperatures. This PBH-dominated phase suppresses the BGW spectrum via entropy dilution and generates a new GW spectrum from PBH density fluctuations. This combined spectrum is detectable at ongoing and planned near-future GW detectors and exhibits a unique shape with a low-frequency peak explaining PTA data, a mid-range dip, and a sharp peak followed by a third peak at high-frequency. This distinctive shape sets it apart from spectra generated by other matter dominations or exotic physics. Therefore, while important for studying GWs in the nHz range, the recent PTA result also sets the stage for testing and constraining various well-studied mechanisms following a PBH domination, using low-frequency measurements and correlated observations of unique high-frequency GW spectral features.