{
  "abstract": "We derive explicit expressions for the primordial scalar and tensor spectra at arbitrary finite order $p$ in the slow-roll expansion, valid both for canonical single-field inflation and $k$-inflation. At any order, the spectra are determined by known combinations of slow-roll parameters weighted by universal coefficients entirely fixed by the free de Sitter solutions, without requiring perturbatively corrected mode functions. Using these spectra, we obtain closed-form consistency relations that connect the tensor tilt $n_t$ and its runnings $α_n^t\\equiv d^n n_t/d(\\ln k)^n$ to the tensor-to-scalar ratio $r$, the scalar spectral index $n_s$, and its runnings $α_n^s\\equiv d^n(n_s-1)/d(\\ln k)^n$. The consistency relations are valid for arbitrary $n\\geq 0$ and any finite $p\\geq 0$, without recursion over lower-order relations. For $k$-inflation, they additionally depend on the scalar sound speed and its scale derivatives. We develop an algorithm that generates both the spectra and consistency relations for any pair $(n,p)$. We reproduce known results through next-to-next-to-next-to-leading order (N3LO) and extend the explicit calculations up to N10LO.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28608",
  "author_total": 1,
  "authors": [
    {
      "name": "William Giarè"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7ptt2q1nrscsj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28608",
  "fulltext_url": null,
  "id": "7ptt2q1nrscsj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28608",
  "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"
    ],
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3103|Cosmology and Gravitation Theories"
    ]
  ],
  "openalex": "W7223140883",
  "pdf_url": "https://arxiv.org/pdf/2610.28608",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7ptt2q1nrscsj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.28608",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28608"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.CO",
      "subfield": "cosmology"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Slow-Roll Inflation at Arbitrary Order",
  "title_text": "Slow-Roll Inflation at Arbitrary Order",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:04Z",
  "url": "https://research.draconitic.com/paper/7ptt2q1nrscsj",
  "venue": "arXiv",
  "versions": []
}