{
  "abstract": "We investigate the question of equivalence between the Einstein and Jordan frames for generic scalar-tensor and $f(R)$ gravity theories in the context of minisuperspace quantum cosmology. We consider, particularly, the minisuperspace of a homogeneous and isotropic universe with the Friedmann-Lemaître-Robertson-Walker metric. We show that the equivalence between the frames depends on the operator ordering scheme of the quantum Hamiltonian: if the quantum theory is covariant under point canonical transformations in the minisuperspace, then the equivalence between the two frames holds. We find that for a large class of operator orderings, including the Laplace-Beltrami operator in the minisuperspace, the wave functions of the universe obtained in the two frames are related by the same transformations that connect the two frames, \\textit{i.e.}, the frames are quantum mechanically equivalent. Further, we show that adding a fluid clock with an arbitrary equation of state parameter $w$ to the system breaks the equivalence, except for the case of a radiation fluid ($w=1/3$). All our arguments are presented at a formal level in both canonical and path integral approaches, and for any scalar-tensor, $f(R)$ theories without assuming any particular model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23785",
  "author_total": 3,
  "authors": [
    {
      "name": "Vikramaditya Mondal"
    },
    {
      "name": "Sumanta Chakraborty"
    },
    {
      "name": "Soumitra SenGupta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1fbx0qnxbk2b8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23785",
  "fulltext_url": null,
  "id": "1fbx0qnxbk2b8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23785",
  "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",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3103|Cosmology and Gravitation Theories"
    ]
  ],
  "openalex": "W7214020861",
  "pdf_url": "https://arxiv.org/pdf/2609.23785",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1fbx0qnxbk2b8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.23785",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23785"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Equivalence of the wave function of the universe in the Einstein and Jordan frames",
  "title_text": "Equivalence of the wave function of the universe in the Einstein and Jordan frames",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/1fbx0qnxbk2b8",
  "venue": "arXiv",
  "versions": []
}