E-models of inflation and primordial black holes

We propose and study the new (generalized) E-type $\alpha$-attractor models of inflation, in order to include formation of primordial black holes (PBHs). The inflaton potential has a near-inflection point where slow-roll conditions are violated, thus leading to large scalar perturbations collapsing to PBHs later. An ultra-slow roll (short) phase exists between two (longer) phases of slow-roll inflation. We numerically investigate the phases of inflation, derive the power spectrum of scalar perturbations and calculate the PBHs masses. For certain values of the parameters, the asteroid-size PBHs can be formed with the masses of $10^{17}\div 10^{19}$ g, beyond the Hawking evaporation limit and in agreement with current CMB observations. Those PBHs are a candidate for (part of) dark matter in the present universe, while the gravitational waves induced by the PBHs formation may be detectable by the future space-based gravitational interferometers.