The Hartle-Hawking state for toroidal quantum cosmologies is expressed in the Langlands decomposition as a sum over zeta zeros whose near-singularity dynamics follow the Hilbert-Pólya Hamiltonian and as a Möbius average of CFT partition functions.
The Wave Function of Quantum de Sitter
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abstract
We consider quantum general relativity in three dimensions with a positive cosmological constant. The Hartle-Hawking wave function is computed as a function of metric data at asymptotic future infinity. The analytic continuation from Euclidean Anti-de Sitter space provides a natural integration contour in the space of metrics, allowing us -- with certain assumptions -- to compute the wave function exactly, including both perturbative and non-perturbative effects. The resulting wave function is a non-normalizable function of the conformal structure of future infinity which is infinitely peaked at geometries where I^+ becomes infinitely inhomogeneous. We interpret this as a non-perturbative instability of de Sitter space in three dimensional Einstein gravity.
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The no-boundary wavefunction on the 3-torus, summed over SL(3,Z) geometries using GL(3) automorphic forms, favors large inflating universes with N ≳ 250 e-folds and induces torus-moduli corrections to the CMB spectrum.
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M\"obius randomness in the Hartle-Hawking state
The Hartle-Hawking state for toroidal quantum cosmologies is expressed in the Langlands decomposition as a sum over zeta zeros whose near-singularity dynamics follow the Hilbert-Pólya Hamiltonian and as a Möbius average of CFT partition functions.
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Inflation and topology from the no-boundary state
The no-boundary wavefunction on the 3-torus, summed over SL(3,Z) geometries using GL(3) automorphic forms, favors large inflating universes with N ≳ 250 e-folds and induces torus-moduli corrections to the CMB spectrum.