{
  "abstract": "Inflation driven purely by the quantum running of the curvature-squared couplings of quadratic gravity was shown to accommodate the high scalar tilt favored by recent cosmic microwave background observations, starting from a Euclidean four-sphere at a maximum of the running $R^2$ coupling. That maximum exists only in one renormalization scheme, and is not stationary once the Euler trace anomaly is included. We show that the standard one-loop running, with the usually neglected Gauss--Bonnet coefficient retained, recovers the missing de Sitter state: the Euler running balances the scale dependence of the $R^2$ term at a unique coupling ratio, giving a de Sitter solution that is stationary for the gravitational constraint and for the compact Euclidean action alike, and whose scalaron potential is an extremely flat hilltop ($m^2/H^2\\simeq-5\\times10^{-10}$) joined to an inverse-linear inflationary plateau. The last $N_*\\simeq50$--$60$ $e$-folds are scheme independent, with scalar tilt $n_s\\simeq1-4/(3N_*)$, while the tensor-to-scalar ratio, $r$, is set by the number of matter fields that enhance the running. The current tensor bound excludes pure gravity and sets a minimum matter content, some $4\\times10^6$ conformally coupled scalars or $3\\times10^5$ vectors---$2.6$ times fewer than the momentum-induced scheme requires---while one-loop control to the end of inflation sets a maximum about ten times higher. Across that window the model predicts $r\\gtrsim0.008$ with $0.973\\lesssim n_s\\lesssim0.978$, within reach of upcoming CMB polarization surveys.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24912",
  "author_total": 2,
  "authors": [
    {
      "name": "Ruolin Liu"
    },
    {
      "name": "Niayesh Afshordi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9y371g91z5qvt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24912",
  "fulltext_url": null,
  "id": "9y371g91z5qvt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24912",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.CO"
    ],
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3103|Cosmology and Gravitation Theories"
    ]
  ],
  "openalex": "W7214015405",
  "pdf_url": "https://arxiv.org/pdf/2609.24912",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9y371g91z5qvt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.24912",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24912"
    }
  ],
  "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": "Gauss--Bonnet running and the de Sitter saddle of quadratic gravity inflation",
  "title_text": "Gauss--Bonnet running and the de Sitter saddle of quadratic gravity inflation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/9y371g91z5qvt",
  "venue": "arXiv",
  "versions": []
}