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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2506.23571 |
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| _version_ | 1866915608144117760 |
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| author | Raveendran, Rathul Nath |
| author_facet | Raveendran, Rathul Nath |
| contents | We investigate the breakdown of the separate-universe approximation during transitions in transient ultra-slow-roll inflation by analyzing the evolution of the comoving curvature perturbation ${\cal R}$ and its conjugate momentum $Π$. It is well known that spatial gradient terms lead to a failure of this approximation, particularly at the transition from slow-roll to ultra-slow-roll phase. We show that a similar breakdown also occurs during the second transition back to slow-roll when considering the evolution of $Π$. Interestingly, while the homogeneous solution for $Π$ accurately captures the dynamics across the first transition, it is the homogeneous solution for ${\cal R}$ that becomes valid across the second. Furthermore, we demonstrate that the spatial curvature term introduced in the extended $δN$ formalism of \cite{Artigas:2024ajh} can be interpreted as arising from the contribution of $Π$ to the energy density perturbation. Importantly, this modification of the local Hubble parameter is valid only when the first slow-roll parameter is both small and strictly constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23571 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The validity of separate-universe approach in transient ultra-slow-roll inflation Raveendran, Rathul Nath Cosmology and Nongalactic Astrophysics We investigate the breakdown of the separate-universe approximation during transitions in transient ultra-slow-roll inflation by analyzing the evolution of the comoving curvature perturbation ${\cal R}$ and its conjugate momentum $Π$. It is well known that spatial gradient terms lead to a failure of this approximation, particularly at the transition from slow-roll to ultra-slow-roll phase. We show that a similar breakdown also occurs during the second transition back to slow-roll when considering the evolution of $Π$. Interestingly, while the homogeneous solution for $Π$ accurately captures the dynamics across the first transition, it is the homogeneous solution for ${\cal R}$ that becomes valid across the second. Furthermore, we demonstrate that the spatial curvature term introduced in the extended $δN$ formalism of \cite{Artigas:2024ajh} can be interpreted as arising from the contribution of $Π$ to the energy density perturbation. Importantly, this modification of the local Hubble parameter is valid only when the first slow-roll parameter is both small and strictly constant. |
| title | The validity of separate-universe approach in transient ultra-slow-roll inflation |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2506.23571 |