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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Using worldline formalism and geometric quantization, the partition function for 3D gravity with matter on thermal AdS3 is computed via equivariant localization, reproducing the Wilson spool and conjecturing the all-orders result.
Switching to 3-torus topology and summing SL(3,Z) geometries via automorphic forms makes the no-boundary wavefunction favor large inflating universes with over 250 e-folds, plus CMB corrections from torus moduli.
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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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What's the Matter with 3D Gravity?
Using worldline formalism and geometric quantization, the partition function for 3D gravity with matter on thermal AdS3 is computed via equivariant localization, reproducing the Wilson spool and conjecturing the all-orders result.
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Inflation and topology from the no-boundary state
Switching to 3-torus topology and summing SL(3,Z) geometries via automorphic forms makes the no-boundary wavefunction favor large inflating universes with over 250 e-folds, plus CMB corrections from torus moduli.