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Primordial Black Hole Formation in Starobinsky's Linear Potential Model
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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. 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.
Forward citations
Cited by 6 Pith papers
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Nonlinear Lattice Framework for Inflation: Bridging stochastic inflation and the $\delta{N}$ formalism
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An open quantum system treatment of curvature perturbations during Ultra-Slow-Roll inflation shows that environmental decoherence erases the interference dip, modifies the growth slope, and induces oscillatory feature...
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Derives stochastic equations from Schwinger-Keldysh formalism that include quantum diffusion and classical metric perturbations for non-perturbative ultra-slow-roll inflation, validated on Starobinsky and critical Hig...
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Lattice simulations of bumpy axion U(1) inflation in the strong backreaction regime generate curvature perturbations large enough for primordial black holes to comprise all dark matter.
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Hybrid inflation produces enhanced curvature perturbations with a broad power spectrum peak featuring k^3 infrared growth and positive f_NL fixed by tachyonic waterfall geometry, potentially accounting for PBH dark ma...
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