EFT Compatible PBHs: Effective Spawning of the Seeds for Primordial
  Black Holes during Inflation
  Most of the inflationary scenarios that try to explain the origin of
Primordial Black Holes (PBHs) from the enhancements of the power spectrum to
values of order one, at the relevant scales, run into clashes with the
Effective Field Theory (EFT) criteria or fail to enhance the power spectrum to
such large amplitudes. In this paper, we unravel a mechanism for enhancing the
power spectrum during inflation that does not use the flattening of the
potential or reduction of the sound speed of scalar perturbations. The
mechanism is based on this observation in the formalism of Extended EFT of
inflation (EEFToI) with the sixth order polynomial dispersion relation for
scalar perturbations that if the quartic coefficient in the dispersion relation
is negative and smaller than a certain threshold, the amplitude of the power
spectrum is enhanced substantially. The instability mechanism must arrange to
kick in at the scales of interest related to the mass of the PBHs one would
like to produce, which can be ten(s) of solar mass PBHs, suitable for LIGO
events, or $10^{-17}-10^{-13}$ solar mass PBHs, which can comprise the whole
dark matter energy density. We argue that the strong coupling is avoided for
the range of parameters that the mechanisms enhance the power spectrum to the
required amount.
