Small scale induced gravitational waves from primordial black holes, a
  stringent lower mass bound, and the imprints of an early matter to radiation
  transition
  In all inflationary scenarios of primordial black holes (PBH) formation,
amplified scalar perturbations inevitably accompany an induced stochastic
gravitational waves background (ISGWB) at smaller scales. In this paper, we
study the ISGWB originating from the inflationary model, introduced in our
previous paper [1] wherein PBHs can be produced with a nearly monochromatic
mass fraction in the asteroid mass window accounting for the total dark matter
in the universe. We numerically calculate the ISGWB in our scenario for
frequencies ranging from nanoHz to KHz that covers the observational scales
corresponding to future space based GW observatories such as IPTA, LISA, DECIGO
and ET. Interestingly, we find that ultralight PBHs ($M_{\rm PBH} \sim 10^{-20}
M_\odot$) which shall completely evaporate by today with exceedingly small
contribution to dark matter, would still generate an ISGWB that may be detected
by a future design of the ground based Advanced LIGO detector. Using a model
independent approach, we obtain a stringent lower mass limit for ultralight
PBHs which would be valid for a large class of ultra slow roll inflationary
models. Further, we extend our formalism to study the imprints of a reheating
epoch on both the ISGWB and the derived lower mass bound. We find that any
non-instantaneous reheating leads to an even stronger lower bound on PBHs mass
and an epoch of a prolonged matter dominated reheating shifts the ISGWB
spectrum to smaller frequencies. In particular, we show that an epoch of an
early matter dominated phase leads to a secondary amplification of ISGWB at
much smaller scales corresponding to the smallest comoving scale leaving the
horizon during inflation or the end of inflation scale. Finally, we discuss the
prospects of the ISGWB detection by the proposed and upcoming GW observatories.
