One-loop corrections to the E-type <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math>-attractor models of inflation and primordial black hole production

The one-loop corrections (1LC) to the power spectrum of scalar perturbations arising from cubic interactions in the single-field E-type $\ensuremath{\alpha}$-attractor models of inflation and primordial black hole (PBH) production are numerically calculated. The results demonstrate the 1LC contributes merely a few percent to the tree-level power spectrum. The model parameters are chosen to predict the PBH masses in the asteroid-mass range, while maintaining consistency with the cosmic microwave background observations within $1\ensuremath{\sigma}$ confidence levels, and obeying the upper limits on $\ensuremath{\mu}$-distortions. The PBHs formed on scales smaller than the inflation scale can constitute a significant fraction of the present dark matter. The PBH-induced gravitational waves (GW) may be detectable by the future space-based gravitational interferometers. We also consider a reconstruction of the scalar potential from possible GW observations and present a numerical approach tested in the model parameter space.