The no-boundary proposal in biaxial Bianchi IX minisuperspace

Abstract

We implement the no-boundary proposal for the wave function of the universe in an exactly solvable Bianchi IX minisuperspace model with two scale factors. We extend our earlier work (Phys. Rev. Lett. 121, 081302, 2018 / arXiv:1804.01102) to include the contribution from the $\mathbb{C}{\text{P}}^2\setminus B^4$ topology. The resulting wave function yields normalizable probabilities and thus fits into a predictive framework for semiclassical quantum cosmology. We find that the amplitude is low for large anisotropies. In the isotropic limit the usual Hartle-Hawking wave function for the de Sitter minisuperspace model is recovered. Inhomogeneous perturbations in an extended minisuperspace are shown to be initially in their ground state. We also demonstrate that the precise mathematical implementation of the no-boundary proposal as a functional integral in minisuperspace depends on detailed aspects of the model, including the choice of gauge-fixing. This shows in particular that the choice of contour cannot be fundamental, adding weight to the recent proposal that the semiclassical no-boundary wave function should be defined solely in terms of a collection of saddle points. We adopt this approach in most of this paper. Finally we show that the semiclassical tunneling wave function of the universe is essentially equal to the no-boundary state in this particular minisuperspace model, at least in the subset of the classical domain where the former is known.

49+29 pages, 19 figures

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Cited by in corpus (19)

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• Cosmic eggs to relax the cosmological constant
• Truly Lorentzian quantum cosmology
• Bianchi IX geometry and the Einstein-Maxwell theory
• Generalized boundary conditions in closed cosmologies
• Holographic (Eternal) Inflation
• Lorentzian quantum cosmology with torsion
• Jackiw-Teitelboim Gravity and Lorentzian Quantum Cosmology
• Summing over Non-singular Paths in Quantum Cosmology
• Dissipative Emergence of Inflation from Quasi-Cyclic Universe
• Delicate curvature bounces in the no-boundary wave function and in the late universe
• Physical States and Transition Amplitudes in Piecewise Flat Quantum Gravity
• A Quantum Informational Approach to the Problem of Time
• Functional Determinants for Constrained Path Integrals in Minisuperspace Jackiw-Teitelboim Gravity