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arXiv · 2602.19704

Unimodular quantum cosmology in the connection representation: A minimal model

Shinji Yamashita
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Abstract

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 Schr\"odinger-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.

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Shinji Yamashita. 2026-02-23. Unimodular quantum cosmology in the connection representation: A minimal model. https://doi.org/10.1103/rgj9-8r3d

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