Constant roll and non-Gaussian tail in light of logarithmic duality
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913699336290304 |
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| author | Inui, Ryoto Motohashi, Hayato Pi, Shi Tada, Yuichiro Yokoyama, Shuichiro |
| author_facet | Inui, Ryoto Motohashi, Hayato Pi, Shi Tada, Yuichiro Yokoyama, Shuichiro |
| contents | The curvature perturbation in a model of constant-roll (CR) inflation is interpreted in view of the logarithmic duality discovered in Ref. [1] according to the $δN$ formalism. We confirm that the critical value $β:=\ddotφ/(H\dotφ)=-3/2$ determining whether the CR condition is stable or not is understood as the point at which the dual solutions, i.e., the attractor and non-attractor solutions of the field equation, are interchanged. For the attractor-solution domination, the curvature perturbation in the CR model is given by a simple logarithmic mapping of a Gaussian random field, which can realise both the exponential tail (i.e., the single exponential decay) and the Gumbel-distribution-like tail (i.e., the double exponential decay) of the probability density function, depending on the value of $β$. Such a tail behaviour is important for, e.g., the estimation of the primordial black hole abundance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_13500 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constant roll and non-Gaussian tail in light of logarithmic duality Inui, Ryoto Motohashi, Hayato Pi, Shi Tada, Yuichiro Yokoyama, Shuichiro Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Theory The curvature perturbation in a model of constant-roll (CR) inflation is interpreted in view of the logarithmic duality discovered in Ref. [1] according to the $δN$ formalism. We confirm that the critical value $β:=\ddotφ/(H\dotφ)=-3/2$ determining whether the CR condition is stable or not is understood as the point at which the dual solutions, i.e., the attractor and non-attractor solutions of the field equation, are interchanged. For the attractor-solution domination, the curvature perturbation in the CR model is given by a simple logarithmic mapping of a Gaussian random field, which can realise both the exponential tail (i.e., the single exponential decay) and the Gumbel-distribution-like tail (i.e., the double exponential decay) of the probability density function, depending on the value of $β$. Such a tail behaviour is important for, e.g., the estimation of the primordial black hole abundance. |
| title | Constant roll and non-Gaussian tail in light of logarithmic duality |
| topic | Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2409.13500 |