A generalized Hartle-Hawking wavefunction

TL;DR

This paper generalizes the Hartle-Hawking wave function beyond mini-superspace using Fourier duality with the Chern-Simons state, allowing for quantum torsion fluctuations and applying to anisotropic cosmological models.

Contribution

It introduces a formal expression for a generalized wave function beyond mini-superspace, incorporating torsion and applicable to various cosmological models.

Findings

Provides a formal expression for the generalized wave function.

Demonstrates the approach with Bianchi and Kantowski-Sachs models.

Allows quantum torsion fluctuations in the wave function.

Abstract

The Hartle-Hawking wave function is known to be the Fourier dual of the Chern-Simons or Kodama state reduced to mini-superspace, using an integration contour covering the whole real line. But since the Chern-Simons state is a general solution of the Hamiltonian constraint (with a given ordering), its Fourier dual should provide the general solution (i.e. beyond mini-superspace) of the Wheeler DeWitt equation representing the Hamiltonian constraint in the metric representation. We write down a formal expression for such a wave function, to be seen as the generalization beyond mini-superspace of the Hartle-Hawking wave function. Its explicit evaluation (or simplification) depends only on the symmetries of the problem, and we illustrate the procedure with anisotropic Bianchi models and with the Kantowski-Sachs model. A significant difference of this approach is that we may leave the torsion inside the wave functions when we set up the ansatz for the connection, rather than setting it to zero before quantization. This allows for quantum fluctuations in the torsion, with far reaching consequences.