{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/stochastic-inflation-beyond-slow-roll-noise","title":"Stochastic inflation beyond slow roll: noise modelling and importance sampling","arxiv_id":"2410.13683","date":"2024-10-17","proceeding":null,"authors":["Joseph H. P. Jackson","Hooshyar Assadullahi","Andrew D. Gow","Kazuya Koyama","Vincent Vennin","David Wands"],"abstract":"We simulate the distribution of very rare, large excursions in the primordial density field produced in models of inflation in the very early universe which include a strong enhancement of the power spectrum. The stochastic $\\delta \\mathcal{N}$ formalism is used to identify the probability distribution for the primordial curvature perturbation with the first-passage-time distribution, $P(\\delta \\mathcal{N})$, and we compare our stochastic results with those obtained in the classical $\\delta \\mathcal{N}$ approach. We extend the PyFPT numerical code to simulate the full 2D phase space, and apply importance sampling which allows very rare fluctuations to be simulated in $\\mathcal{O}(10)$ minutes on a single CPU, where previous direct simulations required supercomputers. We demonstrate that the stochastic noise due to quantum fluctuations after a sudden transition to ultra-slow roll can be accurately modelled using an analytical Bessel-function ansatz to identify the homogeneous growing mode. The stochastic noise found in this way is a function of the field value only. This enables us to coarse grain the inflation field at the Hubble scale and include non-linear, stochastic evolution on all super-Hubble length scales.","url_abs":"https://arxiv.org/abs/2410.13683v2","url_pdf":"https://arxiv.org/pdf/2410.13683v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"stochastic-inflation-beyond-slow-roll-noise","repo_url":"https://github.com/jacks0nj/pyfpt","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}