Ultra-Slow-Roll Inflation on the Lattice II: Nonperturbative Curvature Perturbation
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| Format: | Preprint |
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2025
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| _version_ | 1866908578605957120 |
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| author | Caravano, Angelo Franciolini, Gabriele Renaux-Petel, Sébastien |
| author_facet | Caravano, Angelo Franciolini, Gabriele Renaux-Petel, Sébastien |
| contents | Building on the recent lattice simulations of ultra-slow-roll (USR) dynamics presented in arXiv:2410.23942, we investigate the role of the nonlinear relation between the inflaton field configuration and the curvature perturbation $ζ$, the key observable after inflation. Using a nonperturbative $δN$ approach applied to the lattice output, we generate fully nonlinear three-dimensional maps of $ζ$. This calculation captures both the non-Gaussianity arising from the nonlinear mapping between $ϕ$ and $ζ$, and the intrinsic non-Gaussianity generated around Hubble crossing by the nonlinear field dynamics, which is neglected in stochastic approaches. We find that the nonlinear mapping has a profound impact on the statistics, significantly enhancing the positive tail of the $ζ$ probability distribution, with important implications for observable quantities. A central part of this work is the comparison with the standard perturbative treatment based on a gauge transformation, which allows us to quantify when and how the perturbative picture breaks down as fluctuations grow large. Together with arXiv:2410.23942, this work sets the basis for robust, nonperturbative predictions of primordial black hole production and scalar-induced gravitational wave emission from inflation using lattice simulations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_11795 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ultra-Slow-Roll Inflation on the Lattice II: Nonperturbative Curvature Perturbation Caravano, Angelo Franciolini, Gabriele Renaux-Petel, Sébastien Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Theory Building on the recent lattice simulations of ultra-slow-roll (USR) dynamics presented in arXiv:2410.23942, we investigate the role of the nonlinear relation between the inflaton field configuration and the curvature perturbation $ζ$, the key observable after inflation. Using a nonperturbative $δN$ approach applied to the lattice output, we generate fully nonlinear three-dimensional maps of $ζ$. This calculation captures both the non-Gaussianity arising from the nonlinear mapping between $ϕ$ and $ζ$, and the intrinsic non-Gaussianity generated around Hubble crossing by the nonlinear field dynamics, which is neglected in stochastic approaches. We find that the nonlinear mapping has a profound impact on the statistics, significantly enhancing the positive tail of the $ζ$ probability distribution, with important implications for observable quantities. A central part of this work is the comparison with the standard perturbative treatment based on a gauge transformation, which allows us to quantify when and how the perturbative picture breaks down as fluctuations grow large. Together with arXiv:2410.23942, this work sets the basis for robust, nonperturbative predictions of primordial black hole production and scalar-induced gravitational wave emission from inflation using lattice simulations. |
| title | Ultra-Slow-Roll Inflation on the Lattice II: Nonperturbative Curvature Perturbation |
| topic | Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2506.11795 |