Comment on: "Third-order corrections to the slow-roll expansion: Calculation and constraints with Planck, ACT, SPT, and BICEP/Keck [2025 PDU 47 101813]"
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| Format: | Preprint |
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2026
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| _version_ | 1866918443622596608 |
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| author | Auclair, Pierre Ringeval, Christophe |
| author_facet | Auclair, Pierre Ringeval, Christophe |
| contents | We point out that several terms in the third-order corrections to the slow-roll power spectra presented by Ballardini et al. [1] are incorrect. The authors of that work claim that their result differ from the ones originally presented by Auclair & Ringeval [2] due to some different approximation schemes. However, in our original work, all terms at all orders have been derived exactly and any difference between two expansions performed at the same pivot wavenumber signals a problem. As we show in this comment, Ballardini et al. [1] have misevaluated some definite three-dimensional integrals by integrating a truncated Taylor expansion instead of Taylor expanding an integral. Our claim is backed-up with a Monte-Carlo numerical integration of the incriminated three-dimensional integrals, which, unsurprisingly, matches the analytical value derived in Auclair & Ringeval [2]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_06521 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Comment on: "Third-order corrections to the slow-roll expansion: Calculation and constraints with Planck, ACT, SPT, and BICEP/Keck [2025 PDU 47 101813]" Auclair, Pierre Ringeval, Christophe Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory We point out that several terms in the third-order corrections to the slow-roll power spectra presented by Ballardini et al. [1] are incorrect. The authors of that work claim that their result differ from the ones originally presented by Auclair & Ringeval [2] due to some different approximation schemes. However, in our original work, all terms at all orders have been derived exactly and any difference between two expansions performed at the same pivot wavenumber signals a problem. As we show in this comment, Ballardini et al. [1] have misevaluated some definite three-dimensional integrals by integrating a truncated Taylor expansion instead of Taylor expanding an integral. Our claim is backed-up with a Monte-Carlo numerical integration of the incriminated three-dimensional integrals, which, unsurprisingly, matches the analytical value derived in Auclair & Ringeval [2]. |
| title | Comment on: "Third-order corrections to the slow-roll expansion: Calculation and constraints with Planck, ACT, SPT, and BICEP/Keck [2025 PDU 47 101813]" |
| topic | Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.06521 |