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.
Hervik, Class
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abstract
The minisuperspace model of a Bianchi Type I universe with compact spatial sections is investigated. The classical solutions are brought onto a form were the difference between compact and infinite spatial sections are manifest. One of the features of the compact case is that it has a non-trivial moduli space. The solution space of the compact Bianchi Type I universe is 10 dimensional whereas the Kasner solutions only have a 1 dimensional solution space. We also include the classical solutions with dust and a cosmological constant. Solutions to the Wheeler-DeWitt equation are obtained in light of the tunneling boundary proposal by Vilenkin. Backreaction effects from a simple scalar field are also investigated.
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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.
All minisuperspaces from symmetry reductions of the Einstein-Hilbert Lagrangian that obey the principle of symmetric criticality are canonically quantized and their Wheeler-DeWitt equations are solved.
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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.
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Canonical quantization of all minisuperspaces with consistent symmetry reductions
All minisuperspaces from symmetry reductions of the Einstein-Hilbert Lagrangian that obey the principle of symmetric criticality are canonically quantized and their Wheeler-DeWitt equations are solved.