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arXiv · 2303.00341

Note on the bispectrum and one-loop corrections in single-field inflation with primordial black hole formation

Jason Kristiano·Jun'ichi Yokoyama
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Abstract

Primordial black holes can be formed from the collapse of large-amplitude perturbation on small scales in the early Universe. Such an enhanced spectrum can be realized by introducing a flat region in the potential of single-field inflation, which makes the inflaton go into a temporary ultraslow-roll period. In this paper, we calculate the bispectrum of curvature perturbation in such a scenario. We explicitly confirm that bispectrum satisfies Maldacena's theorem. At the end of the ultraslow-roll period, the bispectrum is generated by bulk interaction and field redefinition. At the end of inflation, bispectrum is generated only by bulk interaction. We also calculate the one-loop correction to the power spectrum from the bispectrum, called the source method. We find it consistent with the calculation of the one-loop correction from the second-order expansion of in-in perturbation theory.

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Jason Kristiano, Jun'ichi Yokoyama. 2023-03-01. Note on the bispectrum and one-loop corrections in single-field inflation with primordial black hole formation. https://doi.org/10.1103/physrevd.109.103541

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