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.