Proving the absence of large one-loop corrections to the power spectrum of curvature perturbations in transient ultra-slow-roll inflation within the path-integral approach
Abstract We revisit one-loop corrections to the power spectrum of curvature perturbations ζ in an inflationary scenario containing a transient ultra-slow-roll (USR) period. In ref. [1], it was argued that one-loop corrections to the power spectrum of ζ can be larger than the tree-level one within th...
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SpringerOpen
2024-12-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP12(2024)095 |
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| author | Ryodai Kawaguchi Shinji Tsujikawa Yusuke Yamada |
| author_facet | Ryodai Kawaguchi Shinji Tsujikawa Yusuke Yamada |
| author_sort | Ryodai Kawaguchi |
| collection | DOAJ |
| description | Abstract We revisit one-loop corrections to the power spectrum of curvature perturbations ζ in an inflationary scenario containing a transient ultra-slow-roll (USR) period. In ref. [1], it was argued that one-loop corrections to the power spectrum of ζ can be larger than the tree-level one within the parameter region generating the seeds of primordial black holes during the USR epoch, which implies the breakdown of perturbation theory. We prove that this is not the case by using a master formula for one-loop corrections to the power spectrum obtained in ref. [2]. We derive the same formula within the path-integral formalism, which is simpler than the original derivation in [2]. To show the smallness of one-loop corrections, the consistency relations and the effective constancy of tree-level mode functions of ζ for super-Hubble modes play essential roles, with which the master formula gives a simple expression for one-loop corrections. For concreteness, we provide a reduced set of interactions including the leading-order one, while establishing the consistency relations in a self-consistent manner. We also show how the consistency relations of various operators hold explicitly, which plays a key role in proving the absence of large one-loop corrections. |
| format | Article |
| id | doaj-art-e3c2856b2fb44710b51a01ea8e42763d |
| institution | OA Journals |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-e3c2856b2fb44710b51a01ea8e42763d2025-08-20T01:57:11ZengSpringerOpenJournal of High Energy Physics1029-84792024-12-0120241216610.1007/JHEP12(2024)095Proving the absence of large one-loop corrections to the power spectrum of curvature perturbations in transient ultra-slow-roll inflation within the path-integral approachRyodai Kawaguchi0Shinji Tsujikawa1Yusuke Yamada2Department of Physics, Waseda UniversityDepartment of Physics, Waseda UniversityWaseda Institute for Advanced Study, Waseda UniversityAbstract We revisit one-loop corrections to the power spectrum of curvature perturbations ζ in an inflationary scenario containing a transient ultra-slow-roll (USR) period. In ref. [1], it was argued that one-loop corrections to the power spectrum of ζ can be larger than the tree-level one within the parameter region generating the seeds of primordial black holes during the USR epoch, which implies the breakdown of perturbation theory. We prove that this is not the case by using a master formula for one-loop corrections to the power spectrum obtained in ref. [2]. We derive the same formula within the path-integral formalism, which is simpler than the original derivation in [2]. To show the smallness of one-loop corrections, the consistency relations and the effective constancy of tree-level mode functions of ζ for super-Hubble modes play essential roles, with which the master formula gives a simple expression for one-loop corrections. For concreteness, we provide a reduced set of interactions including the leading-order one, while establishing the consistency relations in a self-consistent manner. We also show how the consistency relations of various operators hold explicitly, which plays a key role in proving the absence of large one-loop corrections.https://doi.org/10.1007/JHEP12(2024)095Cosmological modelsde Sitter space |
| spellingShingle | Ryodai Kawaguchi Shinji Tsujikawa Yusuke Yamada Proving the absence of large one-loop corrections to the power spectrum of curvature perturbations in transient ultra-slow-roll inflation within the path-integral approach Journal of High Energy Physics Cosmological models de Sitter space |
| title | Proving the absence of large one-loop corrections to the power spectrum of curvature perturbations in transient ultra-slow-roll inflation within the path-integral approach |
| title_full | Proving the absence of large one-loop corrections to the power spectrum of curvature perturbations in transient ultra-slow-roll inflation within the path-integral approach |
| title_fullStr | Proving the absence of large one-loop corrections to the power spectrum of curvature perturbations in transient ultra-slow-roll inflation within the path-integral approach |
| title_full_unstemmed | Proving the absence of large one-loop corrections to the power spectrum of curvature perturbations in transient ultra-slow-roll inflation within the path-integral approach |
| title_short | Proving the absence of large one-loop corrections to the power spectrum of curvature perturbations in transient ultra-slow-roll inflation within the path-integral approach |
| title_sort | proving the absence of large one loop corrections to the power spectrum of curvature perturbations in transient ultra slow roll inflation within the path integral approach |
| topic | Cosmological models de Sitter space |
| url | https://doi.org/10.1007/JHEP12(2024)095 |
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