M\"obius randomness in the Hartle-Hawking state
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.
Cite
@article{arxiv.2505.03068,
title = {M\"obius randomness in the Hartle-Hawking state},
author = {Victor Godet},
journal= {arXiv preprint arXiv:2505.03068},
year = {2026}
}
Comments
63 pages, 7 figures, v2: typos and minor corrections