Unimodular quantum cosmology in the connection representation: A minimal model
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914344065826816 |
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| author | Yamashita, Shinji |
| author_facet | Yamashita, Shinji |
| contents | We present a quantization of unimodular gravity in the connection representation for a homogeneous, isotropic, and spatially flat cosmological model without matter. In this model, the wave function is governed by a Schrödinger-type equation derived from a reduced phase space approach. Our analysis suggests that, within this minimal setting, the regularity of the operators and the self-adjointness of the Hamiltonian operator are incompatible with a negative cosmological constant. For a positive cosmological constant, the wave functions vanish at zero spatial volume. This behavior emerges as a consequence of enforcing the unimodular condition at the quantum level. Semiclassical fluctuations of the geometry are evaluated and discussed in relation to the cosmological constant problem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_19704 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Unimodular quantum cosmology in the connection representation: A minimal model Yamashita, Shinji General Relativity and Quantum Cosmology We present a quantization of unimodular gravity in the connection representation for a homogeneous, isotropic, and spatially flat cosmological model without matter. In this model, the wave function is governed by a Schrödinger-type equation derived from a reduced phase space approach. Our analysis suggests that, within this minimal setting, the regularity of the operators and the self-adjointness of the Hamiltonian operator are incompatible with a negative cosmological constant. For a positive cosmological constant, the wave functions vanish at zero spatial volume. This behavior emerges as a consequence of enforcing the unimodular condition at the quantum level. Semiclassical fluctuations of the geometry are evaluated and discussed in relation to the cosmological constant problem. |
| title | Unimodular quantum cosmology in the connection representation: A minimal model |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2602.19704 |