Primordial black hole formation in inflationary $\alpha$-attractor
  models
  The formation of primordial black holes is studied using superconformal
inflationary $\alpha$-attractors. An inflaton potential is constructed with a
plateau-like region which brings about the onset of an ultra slow-roll region
where the required enhancement in the curvature power spectrum takes place.
This is accomplished by carefully fine-tuning the parameters in the potential.
For the parameter sets, the amount of observable inflation is such that the
curvature perturbation $\mathcal{P}_{\mathcal{R}}$ peaks at $\sim
10^{14}\text{Mpc}^{-1}$, producing PBHs in the mass window $10^{16}\text{g}\leq
M \leq 10^{18}\text{g}$. The reheating period after inflation is taken into
account to determine whether or not PBH formation takes place in such a phase.
Finally, the spectrum of second order gravitational waves, that can arise due
to the curvature perturbation enhancement, is calculated.
