{
  "abstract": "We derive the consistency conditions governing the propagating content of linear shear-free perturbations of Friedmann-Lema\\^ıtre-Robertson-Walker cosmologies in metric $f(R)$ gravity. The divergence of the shear-free constraint is shown to be the total momentum-conservation equation and therefore does not imply geodesic flow. Its projected time derivative instead supplies a nontrivial integrability condition. Scalar, vector, and tensor sectors must then be tested separately. Shear-freeness removes the independent transverse-traceless electric-magnetic Weyl pair, so no ordinary $+$ or $\\times$ tensor gravitational wave survives. The scalaron is not removed algebraically, but its four-variable harmonic system must remain in the time-dependent consistent subspace generated by the shear-free constraint and all of its time derivatives. For a geodesic shear-free congruence in the spatially flat expanding de Sitter patch, this excludes every nonzero fixed comoving scalar harmonic, including the healthy $R+αR^2-2Λ$ model with $α,Λ>0$. Vector modes obey a curvature-dependent global eigenvalue condition whose right-hand side is negative for positive-density matter with $f'>0$ and $1+w>0$; hence no nonzero vector harmonic survives on that branch. The familiar coasting $R^3$ example evades this sign obstruction only because it lies on an $f'<0$ branch. Thus tensor radiation is absent in the imposed shear-free sector, whereas scalar radiation is not excluded kinematically but remains a model- and background-dependent constraint-closure question.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03260",
  "author_total": 2,
  "authors": [
    {
      "name": "Mudhahir Al Ajmi"
    },
    {
      "name": "Amare Abebe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/15fyhwy9y10dk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03260",
  "fulltext_url": null,
  "id": "15fyhwy9y10dk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03260",
  "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",
      "gr-qc"
    ],
    [
      "openalex",
      "3103|Cosmology and Gravitation Theories"
    ]
  ],
  "openalex": "W7208763296",
  "pdf_url": "https://arxiv.org/pdf/2609.03260",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/15fyhwy9y10dk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:31Z",
      "native_id": "2609.03260",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03260"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Constraint closure and gravitational-wave content of shear-free cosmologies in metric f(R) gravity",
  "title_text": "Constraint closure and gravitational-wave content of shear-free cosmologies in metric f(R) gravity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:31Z",
  "url": "https://research.draconitic.com/paper/15fyhwy9y10dk",
  "venue": "arXiv",
  "versions": []
}