New Solutions To The Bianchi IX Wheeler DeWitt Equation And Leading Order Solutions For $Λ$ $\ne$ 0 And A Primordial Magnetic Field (1910.11970v1)

Abstract: New closed form solutions to the Lorentzian signature symmetry reduced Bianchi IX Wheeler DeWitt equation are obtained using a Euclidean-signature semi classical method for Hartle Hawking ordering parameters $ \pm 2\sqrt{33} $ for the wormhole Hamilton-Jacobi solution. Moving past the wormhole case we also compute first order quantum corrections to Bianchi IX wave functions restricted to the $\beta_+$ axis for the 'no boundary' solution and one of the 'arm' solutions. Furthermore, six solutions to the Bianchi IX Euclidean-signature Hamiltonian Jacobi equation for the case when a cosmological constant is present have been found and are used to construct a semi-classical which respects the symmetry of the Bianchi IX potential. Also two additional solutions were found when both a cosmological constant and an aligned primordial magnetic field are present, which are also used to construct a leading order wave function. Furthermore we construct leading order 'excited' states which are restricted to the $\beta_+$ axis for the cases when a cosmological constant and a primordial magnetic field are present. To conclude, we discuss the interesting features of our solutions, and point out how the cosmological constant appears to act as a driver of anisotropy in our Bianchi IX models. The Euclidean-signature semi-classical method used here is applicable to certain field theories as well. Because this semi classical method was able to find new solutions to a heavily studied problem the results in this paper represent significant progress in the Wheeler-DeWitt approach to quantum cosmology and in the application of Euclidean-signature semi classical methods to Lorentzian signature problems in general.