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In order to produce appreciable amount of primordial black holes (PBHs), the squared amplitude of the curvature perturbation must take a large value of \(\mathcal {O}(0.01)\) , namely, seven digits larger than the value observed by cosmic microwave background radiation (CMB) on large scales. Such a large fluctuation can be achieved by violating the slow-roll (SR) condition within a short duration. The best known of such possibilities is the ultraslow-roll (USR) inflation. We calculate the power spectrum of curvature perturbation in a simple single-field inflation model which evolves through the SR-USR-SR regimes so that both large-amplitude small-scale fluctuation for PBH formation and small-amplitude large-scale fluctuation as observed by CMB are realized. We further calculate the bispectrum and one-loop correction to the power spectrum induced by the third-order action of curvature perturbation as the beginning of precision cosmology on small scales. As a result, we argue that single-field inflationary models realizing PBH formation can be constrained by the quantum correction.

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Generating Large Primordial Fluctuations in Single-Field Inflation for Primordial Black Hole Formation

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  • 发表日期：

    2025年

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  • Jason Kristiano,
  • Jun’ichi Yokoyama

摘要

In order to produce appreciable amount of primordial black holes (PBHs), the squared amplitude of the curvature perturbation must take a large value of \(\mathcal {O}(0.01)\) , namely, seven digits larger than the value observed by cosmic microwave background radiation (CMB) on large scales. Such a large fluctuation can be achieved by violating the slow-roll (SR) condition within a short duration. The best known of such possibilities is the ultraslow-roll (USR) inflation. We calculate the power spectrum of curvature perturbation in a simple single-field inflation model which evolves through the SR-USR-SR regimes so that both large-amplitude small-scale fluctuation for PBH formation and small-amplitude large-scale fluctuation as observed by CMB are realized. We further calculate the bispectrum and one-loop correction to the power spectrum induced by the third-order action of curvature perturbation as the beginning of precision cosmology on small scales. As a result, we argue that single-field inflationary models realizing PBH formation can be constrained by the quantum correction.