A No-Go Theorem for Quantum Cosmologies with Non-natural Hamiltonians
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910218221256704 |
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| author | Dantas, Christine C. |
| author_facet | Dantas, Christine C. |
| contents | 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 a kinematical no-go theorem: non-quadratic cosmological dynamics cannot be geometrized via ED constructions. Quantum-corrected bounce models therefore illustrate a structural limitation of metric geometrization within the ED framework. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_13921 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A No-Go Theorem for Quantum Cosmologies with Non-natural Hamiltonians Dantas, Christine C. General Relativity and Quantum Cosmology 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 a kinematical no-go theorem: non-quadratic cosmological dynamics cannot be geometrized via ED constructions. Quantum-corrected bounce models therefore illustrate a structural limitation of metric geometrization within the ED framework. |
| title | A No-Go Theorem for Quantum Cosmologies with Non-natural Hamiltonians |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2605.13921 |