Note on the bispectrum and one-loop corrections in single-field inflation with primordial black hole formation
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911891370016768 |
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| author | Kristiano, Jason Yokoyama, Jun'ichi |
| author_facet | Kristiano, Jason Yokoyama, Jun'ichi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_00341 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Note on the bispectrum and one-loop corrections in single-field inflation with primordial black hole formation Kristiano, Jason Yokoyama, Jun'ichi High Energy Physics - Theory Cosmology and Nongalactic Astrophysics 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. |
| title | Note on the bispectrum and one-loop corrections in single-field inflation with primordial black hole formation |
| topic | High Energy Physics - Theory Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2303.00341 |