Primordial Black Hole Formation in Starobinsky's Linear Potential Model

Understand

We study the power spectrum of the comoving curvature perturbation $\cal R$ in the model that glues two linear potentials of different slopes, originally proposed by Starobinsky.

• We find that the enhanced power spectrum reaches its maximum at the wavenumber which is $\pi$ times the junction scale.
• The peak is $\sim2.61$ times larger than the ultraviolet plateau.
• We also show that its near-peak behavior can be well approximated by a constant-roll model, once we define the effective ultra-slow-roll $e$-folding number appropriately by considering the contribution from non-single-clock phase only.