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Abstract This work highlights the crucial role played by the equation of state (EoS) parameter within the context of single field inflation with Multiple Sharp Transitions (MSTs) to untangle the current state of the PBH overproduction issue. The situation is examined for a broad interval of EoS parameter that remains most favorable to explain the recent data released by the pulsar timing array (PTA) collaboration. The analysis yields the interval, , to be the most acceptable window from the SIGW interpretation of the PTA signal and where sizeable PBHs abundance, , is observed. It is also found , radiation‐dominated era, to be the best scenario to explain the early stages of the Universe and address the overproduction problem. Within the range of , a regularized‐renormalized‐resummed scalar power spectrum is constructed whose amplitude obeys the perturbativity criterion while being substantial enough to generate EoS dependent scalar induced gravitational waves (‐SIGWs) consistent with NANOGrav‐15 data. For both , the case is found to be more favorable for generating large mass PBHs, , as potential dark matter candidates with substantial abundance after constraints coming from microlensing experiments.
Choudhury et al. (Thu,) studied this question.