{"paper":{"title":"A No-Go Theorem for Quantum Cosmologies with Non-natural Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Non-quadratic cosmological dynamics cannot be geometrized via Eisenhart-Duval lifts.","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Brazil), Christine C. Dantas (Astrophysics Division, INPE","submitted_at":"2026-05-13T14:04:30Z","abstract_excerpt":"The Eisenhart-Duval lift (ED) geometrizes classical dynamics by embedding their trajectories into null geodesics of a higher-dimensional Lorentzian spacetime. However, such a construction requires a natural Hamiltonian, that is, quadratic in the canonical momenta. As a consequence, mini-superspace cosmological models governed by non-natural Hamiltonians cannot admit an ED lift. Effective models in Loop Quantum Cosmology provide a concrete example: polymer-modified Hamiltonians become non-polynomial in the momenta and therefore fall outside the metric framework of the ED lift. We thus establish"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We thus establish a kinematical no-go theorem: non-quadratic cosmological dynamics cannot be geometrized via ED constructions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The Eisenhart-Duval lift applies exclusively to natural Hamiltonians that are quadratic in the canonical momenta, and that polymer-modified Hamiltonians in loop quantum cosmology are genuinely non-polynomial in those momenta.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Non-quadratic Hamiltonians in cosmological models prevent geometrization via the Eisenhart-Duval lift.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Non-quadratic cosmological dynamics cannot be geometrized via Eisenhart-Duval lifts.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"856f60bd57801bd32571df2009dfaa683f50de29393d668fc9cab786811dae0e"},"source":{"id":"2605.13921","kind":"arxiv","version":1},"verdict":{"id":"1ef50b54-e66a-4ea5-aa57-bbfe4dcd7ce5","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:54:40.682963Z","strongest_claim":"We thus establish a kinematical no-go theorem: non-quadratic cosmological dynamics cannot be geometrized via ED constructions.","one_line_summary":"Non-quadratic Hamiltonians in cosmological models prevent geometrization via the Eisenhart-Duval lift.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The Eisenhart-Duval lift applies exclusively to natural Hamiltonians that are quadratic in the canonical momenta, and that polymer-modified Hamiltonians in loop quantum cosmology are genuinely non-polynomial in those momenta.","pith_extraction_headline":"Non-quadratic cosmological dynamics cannot be geometrized via Eisenhart-Duval lifts."},"references":{"count":29,"sample":[{"doi":"","year":1928,"title":"Eisenhart L P 1928 Annals of Mathematics 30 591–606 ISSN 0003486X, 19398980 URL http: //www.jstor.org/stable/1968307","work_id":"3cb961b2-f049-4df5-a96d-1073f10b1ede","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1103/physrevd.31.1841","year":1985,"title":"Duval , author G","work_id":"dc3938c9-cb69-46b1-add8-55d256d8f762","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1103/physrevd.43.3907","year":1991,"title":"Celestial mechanics, conformal structures, and gravitational waves","work_id":"ab620f82-10ed-484b-bc11-679f32985489","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1007/s10773-024-05673-0","year":null,"title":"Duval C, Henkel M, Horvathy P A, Rouhani S and Zhang P M 2024International Journal of Theoret- ical Physics 63 184 (Preprint 2403.20316) URL https://doi.org/10.1007/s10773-024-05673-0","work_id":"8c8bf4c1-9fcd-4973-b412-64723e512775","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1088/0143-0807/36/2/025018","year":2015,"title":"Cariglia M and Alves F K 2015 European Journal of Physics 36 025018 URL https://doi.org/ 10.1088/0143-0807/36/2/025018","work_id":"1d2715ab-69bc-41fb-906a-0384bbc28da0","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":29,"snapshot_sha256":"54a84cadd32a1a528efb0757561411a52916d9951e07179a426960856ac7a160","internal_anchors":5},"formal_canon":{"evidence_count":2,"snapshot_sha256":"f6757dac26643c2e35e614eef646ce33ecda09c7dc8ca74c76fd3c4d60472981"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}