A generalized Hartle-Hawking wavefunction

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.

15 pages, 2 figures, journal version

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• Lorentzian quantum cosmology with torsion
• Torsion and the Probability of Inflation
• Canonical analysis of covariant unimodular gravity and an extension of the Kodama state
• A Realist Interpretation of Unitarity in Quantum Gravity
• Novel phenomena of the Hartle-Hawking wave function
• Particles, Forces and the Early Universe