Novel phenomena of the Hartle-Hawking wave function

Abstract

We find a novel phenomenon in the solution to the Wheeler-DeWitt equation by solving numerically the equation assuming $O(4)$-symmetry and imposing the Hartle-Hawking wave function as a boundary condition. In the slow-roll limit, as expected, the numerical solution gives the most dominant steepest-descent that describes the probability distribution for the initial condition of a universe. The probability is consistent with the Euclidean computations, and the overall shape of the wave function is compatible with analytical approximations, although there exist novel differences in the detailed probability computation. Our approach gives an alternative point of view of the no-boundary wave function from the wave function point of view. Possible interpretations and conceptual issues of this wave function are discussed.

arXiv comment11 pages, 5 figures

References in corpus (9)

• Approaches to Quantum Cosmology
• The Classical Universes of the No-Boundary Quantum State
• The No-Boundary Measure of the Universe
• Review of the No-Boundary Wave Function
• Hawking-Moss bounces and vacuum decay rates
• The no-boundary measure in string theory: Applications to moduli stabilization, flux compactification, and cosmic landscape
• The no-boundary measure in scalar-tensor gravity
• Annihilation-to-nothing: DeWitt boundary condition inside a black hole
• A generalized Hartle-Hawking wavefunction