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.
The Classical Universes of the No-Boundary Quantum State
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abstract
We analyze the origin of the quasiclassical realm from the no-boundary proposal for the universe's quantum state in a class of minisuperspace models. The models assume homogeneous, isotropic, closed spacetime geometries, a single scalar field moving in a quadratic potential, and a fundamental cosmological constant. The allowed classical histories and their probabilities are calculated to leading semiclassical order. We find that for the most realistic range of parameters analyzed a minimum amount of scalar field is required, if there is any at all, in order for the universe to behave classically at late times. If the classical late time histories are extended back, they may be singular or bounce at a finite radius. The ensemble of classical histories is time symmetric although individual histories are generally not. The no-boundary proposal selects inflationary histories, but the measure on the classical solutions it provides is heavily biased towards small amounts of inflation. However, the probability for a large number of efoldings is enhanced by the volume factor needed to obtain the probability for what we observe in our past light cone, given our present age. Our results emphasize that it is the quantum state of the universe that determines whether or not it exhibits a quasiclassical realm and what histories are possible or probable within that realm.
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Timelike Liouville disk path integrals in fixed K-representation produce Hartle-Hawking-like states, a conjecture for all-loop wavefunctions, and a K-independent inner product for 2D quantum cosmology.
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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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Quantum Liouville Cosmology
Timelike Liouville disk path integrals in fixed K-representation produce Hartle-Hawking-like states, a conjecture for all-loop wavefunctions, and a K-independent inner product for 2D quantum cosmology.