Primordial Black Hole Formation in Starobinsky's Linear Potential Model

Abstract

We study the power spectrum of the comoving curvature perturbation R\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 π\pi times the junction scale. The peak is 2.61\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 ee-folding number appropriately by considering the contribution from non-single-clock phase only. Such an abrupt transition to non-attractor phase can leave some interesting characteristic features in the energy spectrum of the scalar-induced gravitational waves, which are detectable in the space-borne interferometers if the primordial black holes generated at such a high peak are all the dark matter.Comment: 45 pages, 8 figure

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