Möbius randomness in the Hartle-Hawking state
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911653484822528 |
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| author | Godet, Victor |
| author_facet | Godet, Victor |
| contents | We consider quantum cosmology for toroidal universes in d+1 dimensions. The Hilbert space is the space of square-integrable automorphic forms for GL(d). The Hartle-Hawking state is defined as a Poincaré sum over the no-boundary geometries. We obtain its representation in the Langlands spectral decomposition. This leads to an expression as a sum over the Riemann zeta zeros and implies that its near singularity dynamics is governed by the Hilbert-Pólya Hamiltonian. It also takes the form of a Möbius average of CFT partition functions which suggests a similar interpretation for the de Sitter entropy. We briefly discuss the relationship between quantum cosmology and the Langlands program. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03068 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Möbius randomness in the Hartle-Hawking state Godet, Victor High Energy Physics - Theory General Relativity and Quantum Cosmology We consider quantum cosmology for toroidal universes in d+1 dimensions. The Hilbert space is the space of square-integrable automorphic forms for GL(d). The Hartle-Hawking state is defined as a Poincaré sum over the no-boundary geometries. We obtain its representation in the Langlands spectral decomposition. This leads to an expression as a sum over the Riemann zeta zeros and implies that its near singularity dynamics is governed by the Hilbert-Pólya Hamiltonian. It also takes the form of a Möbius average of CFT partition functions which suggests a similar interpretation for the de Sitter entropy. We briefly discuss the relationship between quantum cosmology and the Langlands program. |
| title | Möbius randomness in the Hartle-Hawking state |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2505.03068 |