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In all inflationary scenarios of primordial black holes (PBH) formation,amplified scalar perturbations inevitably accompany an induced stochasticgravitational waves background (ISGWB) at smaller scales. In this paper, westudy the ISGWB originating from the inflationary model, introduced in ourprevious paper [1] wherein PBHs can be produced with a nearly monochromaticmass fraction in the asteroid mass window accounting for the total dark matterin the universe. We numerically calculate the ISGWB in our scenario forfrequencies ranging from nanoHz to KHz that covers the observational scalescorresponding to future space based GW observatories such as IPTA, LISA, DECIGOand ET. Interestingly, we find that ultralight PBHs ($M_{\rm PBH} \sim 10^{-20}M_\odot$) which shall completely evaporate by today with exceedingly smallcontribution to dark matter, would still generate an ISGWB that may be detectedby a future design of the ground based Advanced LIGO detector. Using a modelindependent approach, we obtain a stringent lower mass limit for ultralightPBHs which would be valid for a large class of ultra slow roll inflationarymodels. Further, we extend our formalism to study the imprints of a reheatingepoch on both the ISGWB and the derived lower mass bound. We find that anynon-instantaneous reheating leads to an even stronger lower bound on PBHs massand an epoch of a prolonged matter dominated reheating shifts the ISGWBspectrum to smaller frequencies. In particular, we show that an epoch of anearly matter dominated phase leads to a secondary amplification of ISGWB atmuch smaller scales corresponding to the smallest comoving scale leaving thehorizon during inflation or the end of inflation scale. Finally, we discuss theprospects of the ISGWB detection by the proposed and upcoming GW observatories.

physical review. d/physical review. d.

Small scale induced gravitational waves from primordial black holes, a  stringent lower mass bound, and the imprints of an early matter to radiation  transition