{
  "abstract": "The CMB constrains the gravitational constant $G$ at recombination to a few percent of its laboratory value, but the effect of $G$ on recombination itself is usually absorbed into a global fit rather than made explicit. We return to the semi-analytic description of the acoustic spectrum to ask how the acoustic scale $\\ell_A$, the equality scale $\\ell_{\\rm eq}$ and the damping scale $\\ell_{\\rm damp}$ respond to a variation of $G$ during recombination, and where $G$ enters the residual ionization of the dark ages. We use a modified version of CLASS in which $G$ is varied through $λ_G \\equiv \\sqrt{G/G_{\\rm N}}$, scanning $λ_G \\in [0.25,2]$ at fixed physical densities and CMB temperature, with helium recomputed for each model. Analytic rate arguments are confronted with the numerical ionization histories, the visibility function, the Hu & White damping integral and the TT spectra. While $\\ell_{\\rm eq}$ and $\\ell_A$ are nearly independent of $G$, non-equilibrium recombination gives $\\ell_{\\rm damp} \\propto λ_G^{-0.304}$. The dependence exists only above a critical value of $G$, set by fundamental and cosmological parameters, a factor of 49 below $G_{\\rm N}$. The dark-ages optical depth varies by only 16% for $G$ multiplied by 64, a negligible channel. Because $G$ enters only through the expansion rate, the imprint comes entirely from out-of-equilibrium recombination, and the competition between the atomic rates and the expansion is governed by one dimensionless combination, $α_G \\equiv G m_e μ/\\hbar c$, with $μ$ the mean mass of matter per photon. Each scale is the distance to last scattering divided by a length imprinted before it, so a late-time change of gravity rescales all three alike. The ratio $\\ell_{\\rm damp}/\\ell_A$ therefore isolates $G$ at recombination and, up to lensing and screening, compares it directly with the laboratory value.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22128",
  "author_total": 6,
  "authors": [
    {
      "name": "Brahim Lamine"
    },
    {
      "name": "Sébastien Beauchamp"
    },
    {
      "name": "Alain Blanchard"
    },
    {
      "name": "Jehanne Delhomelle"
    },
    {
      "name": "Raphaël Kou"
    },
    {
      "name": "James Rich"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ab9faegsbkfnn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22128",
  "fulltext_url": null,
  "id": "ab9faegsbkfnn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22128",
  "language": "en",
  "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"
    ],
    [
      "hal",
      "0.phys"
    ],
    [
      "hal",
      "1.phys.astr"
    ],
    [
      "openalex",
      "3103|Cosmology and Gravitation Theories"
    ]
  ],
  "openalex": "W7222730048",
  "pdf_url": "https://arxiv.org/pdf/2610.22128",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ab9faegsbkfnn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2610.22128",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22128"
    },
    {
      "first_seen": "2026-11-03T12:20:19Z",
      "native_id": "hal-05849743",
      "source": "hal",
      "url": "https://hal.science/hal-05849743v1"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.CO",
      "subfield": "cosmology"
    },
    {
      "field": "physics",
      "origin": "hal:0.phys",
      "subfield": "general"
    }
  ],
  "title": "The gravitational constant and the cosmic microwave background",
  "title_text": "The gravitational constant and the cosmic microwave background",
  "type": "preprint",
  "updated_at": "2026-11-04T12:20:50Z",
  "url": "https://research.draconitic.com/paper/ab9faegsbkfnn",
  "venue": "arXiv",
  "versions": []
}