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arXiv · 2405.09833

Quantum cosmology as automorphic dynamics

Victor Godet
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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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Victor Godet. 2024-05-16. Quantum cosmology as automorphic dynamics. https://arxiv.org/abs/2405.09833

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