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Quantum cosmology as automorphic dynamics

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arxiv 2405.09833 v2 pith:QPBLA6OP submitted 2024-05-16 hep-th gr-qc

Victor Godet This is my paper · ORCID
classification hep-thgr-qc
keywords dynamicsautomorphiccosmologyfunctionparticlequantumanalyticapplication
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We revisit pure quantum cosmology in three dimensions. The Wheeler-DeWitt equation can be solved perturbatively and the dynamics reduces to a particle on moduli space. Its time evolution is equivalent to the $T\overline{T}$ deformation. Focusing on spacetimes with torus slices, we show that inflationary cosmologies correspond to particle trajectories in Artin's billiard. The resulting automorphic dynamics is developed both from a first and second quantized perspectives. Our main application is to give an interpretation for the Hartle-Hawking state which is here the analytic continuation of the Maloney-Witten partition function. We obtain its spectral decomposition and an exact representation as an average involving the M\"obius function.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Norm of the no-boundary state

    hep-th 2025-06 conditional novelty 7.0 of 10

    At one loop and late time, the norm of the Hartle-Hawking no-boundary state vanishes as e^{S0}/(vol(SO(d,1)) S0^{d(d+1)/4}), and adding an observer stabilizes it to a large positive value.

  2. Wavefunctions of AdS$_3$ Universes and $T\bar{T}$-deformed Torus Partition Functions

    hep-th 2026-08 reject novelty 6.0 of 10

    The paper's central claim of an invertible bulk-boundary transform for T-Tbar deformed torus partition functions is broken by an incorrect inverse kernel and a factor-of-pi normalization inconsistency.

  3. Cosmological correlators in gravitationally-constrained de Sitter states

    hep-th 2025-07 conditional novelty 6.0 of 10

    Cosmological correlators in gravitationally constrained de Sitter states are conformally invariant and differ from QFT vacuum correlators, but relational observables with a heavy background state can reproduce QFT results.

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