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arXiv · 2505.03068

M\"obius randomness in the Hartle-Hawking state

Victor Godet
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Abstract

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 Poincar\'e 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-P\'olya Hamiltonian. It also takes the form of a M\"obius 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.

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Victor Godet. 2025-05-05. M\"obius randomness in the Hartle-Hawking state. https://arxiv.org/abs/2505.03068

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