Primordial black hole formation in inflationary <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math>-attractor models
Rafid Mahbub
Abstract
The formation of primordial black holes (PBHs) is studied using superconformal inflationary $\ensuremath{\alpha}$ attractors. An inflaton potential is constructed with a plateaulike 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 $\ensuremath{\sim}{10}^{14}\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$, producing PBHs in the mass window $1{0}^{16}\text{ }\text{ }\mathrm{g}\ensuremath{\le}M\ensuremath{\le}{10}^{18}\text{ }\text{ }\mathrm{g}$. 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.