{
  "abstract": "We construct exact solutions for single-field inflaton dynamics without invoking the slow-roll approximation. A suitable change of variables reduces the background equation to an Abel equation of the first kind. Although a generic Abel equation is not analytically solvable, we identify a class of inflaton potentials for which the transformed equation admits exact solutions. The resulting framework contains constant-roll inflation as a special case and also accommodates solutions with a constant second Hubble-flow parameter. We analyze the linear local attractor behavior and superhorizon evolution of these rolling backgrounds. Using the public joint CMB likelihood contours in the $(n_s,r)$ plane, we identify compatible parameter regions and show that one rolling branch can also yield $50\\leq N_*<60$. Direct numerical evolution of the scalar and tensor modes at representative points validates the local-index predictions to better than $7\\times10^{-4}$ in $n_s$ and $2\\times10^{-6}$ in $r$. The exact family extends beyond slow roll, although the observationally selected regions displayed here lie close to the slow-roll regime.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01003",
  "author_total": 5,
  "authors": [
    {
      "name": "Jia-Wei Zhang"
    },
    {
      "name": "Bai-Cian Ke"
    },
    {
      "name": "Yao Yu"
    },
    {
      "name": "Dong-Ze He"
    },
    {
      "name": "Shou-Jia Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/em8n5t21b1pwp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01003",
  "fulltext_url": null,
  "id": "em8n5t21b1pwp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01003",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.CO"
    ],
    [
      "openalex",
      "3103|Cosmology and Gravitation Theories"
    ]
  ],
  "openalex": "W7206151338",
  "pdf_url": "https://arxiv.org/pdf/2609.01003",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/em8n5t21b1pwp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "2609.01003",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01003"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.CO",
      "subfield": "cosmology"
    }
  ],
  "title": "A Class of Exact Single-Field Inflationary Solutions beyond Slow Roll",
  "title_text": "A Class of Exact Single-Field Inflationary Solutions beyond Slow Roll",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:00Z",
  "url": "https://research.draconitic.com/paper/em8n5t21b1pwp",
  "venue": "arXiv",
  "versions": []
}