Bianchi IX and VIII Quantum Cosmology with a Cosmological Constant, Aligned Electromagnetic Field, and Scalar Field

TL;DR

This paper explores how matter sources like electromagnetic and scalar fields influence the quantum behavior of anisotropic cosmological models, revealing new quantum states and demonstrating the effectiveness of semi-classical methods without Wick rotation.

Contribution

It introduces a semi-classical approach to analyze quantum Bianchi IX and VIII models with matter fields, highlighting electromagnetic effects on quantum states without using Wick rotation.

Findings

Electromagnetic fields can create or destroy geometric quantum states.

The scalar field acts as an internal clock in the quantum system.

Semi-classical methods effectively analyze Lorentzian quantum cosmology.

Abstract

We investigate the quantum cosmologies of the Bianchi IX and VIII models when a cosmological constant, aligned electromagnetic field and free scalar field are present. The conserved quantity $p_{\phi}$ associated with our free scalar field results in $\phi$ classically being a quantity which monotonically increases with respect to time, thus allowing it to fulfill the role of an 'emergent' internal clock for our constrained quantum systems. We embark on this investigation to better understand how matter sources can affect general anisotropic quantum cosmologies. To aid us we use the Euclidean-signature semi classical method to obtain our wave functions and analyze them. In addition we study briefly the quantum Taub models when an $e^{ \phi}$ potential and aligned electromagnetic field are present. One of the interesting things we found was that our aligned electromagnetic field, depending on how strong it is, can create or destroy geometric states in our 'excited' state wave functions that quantum Bianchi IX universes can tunnel in and out of. This creation of a state is somewhat similar to how non-commutativity in the minisuperspace variables can cause new quantum states to emerge in the quantum Kantowski-Sachs and Bianchi I models. Our results further show the utility of the Euclidean-signature semi classical method towards tackling Lorentzian signature problems without having to invoke a Wick rotation. This feature of not needing to apply a Wick rotation makes this method potentially very useful for tackling a variety of problems in bosonic relativistic field theory and quantum gravity.