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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.03281 |
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| _version_ | 1866911871976603648 |
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| author | Jackson, Joseph H. P. Assadullahi, Hooshyar Gow, Andrew D. Koyama, Kazuya Vennin, Vincent Wands, David |
| author_facet | Jackson, Joseph H. P. Assadullahi, Hooshyar Gow, Andrew D. Koyama, Kazuya Vennin, Vincent Wands, David |
| contents | The separate-universe approach gives an intuitive way to understand the evolution of cosmological perturbations in the long-wavelength limit. It uses solutions of the spatially-homogeneous equations of motion to model the evolution of the inhomogeneous universe on large scales. We show that the separate-universe approach fails on a finite range of super-Hubble scales at a sudden transition from slow roll to ultra-slow roll during inflation in the very early universe. Such transitions are a feature of inflation models giving a large enhancement in the primordial power spectrum on small scales, necessary to produce primordial black holes after inflation. We show that the separate-universe approach still works in a piece-wise fashion, before and after the transition, but spatial gradients on finite scales require a discontinuity in the homogeneous solution at the transition. We discuss the implications for the $δN$ formalism and stochastic inflation, which employ the separate-universe approximation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03281 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The separate-universe approach and sudden transitions during inflation Jackson, Joseph H. P. Assadullahi, Hooshyar Gow, Andrew D. Koyama, Kazuya Vennin, Vincent Wands, David Cosmology and Nongalactic Astrophysics The separate-universe approach gives an intuitive way to understand the evolution of cosmological perturbations in the long-wavelength limit. It uses solutions of the spatially-homogeneous equations of motion to model the evolution of the inhomogeneous universe on large scales. We show that the separate-universe approach fails on a finite range of super-Hubble scales at a sudden transition from slow roll to ultra-slow roll during inflation in the very early universe. Such transitions are a feature of inflation models giving a large enhancement in the primordial power spectrum on small scales, necessary to produce primordial black holes after inflation. We show that the separate-universe approach still works in a piece-wise fashion, before and after the transition, but spatial gradients on finite scales require a discontinuity in the homogeneous solution at the transition. We discuss the implications for the $δN$ formalism and stochastic inflation, which employ the separate-universe approximation. |
| title | The separate-universe approach and sudden transitions during inflation |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2311.03281 |