Gravitational Wave Signatures of Primordial Black Hole Reheating in Upcoming Interferometry Missions

We investigate the prospects of detecting a stochastic gravitational wave (GW) background from the primordial black hole (PBH) reheating epoch. If PBHs form during a non-standard cosmological phase prior to the radiation-dominated era, they can dominate the energy density of the Universe before evaporating via Hawking radiation. Such PBHs can generate induced GWs that may fall within the detectable range of future interferometry missions: (i) through isocurvature perturbations arising from the inhomogeneous spatial distribution of PBHs, and (ii) through the amplification of adiabatic perturbations triggered by the abrupt transition from PBH domination to radiation domination. We assess the detection prospects of such GW spectra using the signal-to-noise ratio, Fisher forecast analysis, and Markov chain Monte Carlo analysis with mock data from LISA and ET. Our findings reveal that ET exhibits superior sensitivity to both isocurvature- and adiabatic-induced GWs, covering a wide PBH mass range of $M_{\rm in} \in (0.5-4\times 10^7)$ g. However, we find that the relative uncertainties associated with the parameter of the isocurvature source are quite high. LISA, by contrast, is mostly sensitive to the adiabatic source, with $M_{\rm in} \in (2\times10^4-5\times 10^8)$ g. The combined effect of adiabatic and isocurvature sources on ET and LISA provides a multi-stage window into the post-inflationary Universe by constraining PBH mass, energy fraction, and the background equation of state.