Möbius randomness in the Hartle-Hawking state
Year: 2025
Type: preprint
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 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.
Source: arXiv (Cornell University)
Author: Godet, Victor
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6929765723
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