Towards Uncovering Generic Effects Of Matter Sources In Anisotropic Quantum Cosmologies Via Taub Models

TL;DR

This paper analytically solves the Wheeler DeWitt equation for Taub models with matter sources, revealing infinite excited states and multiple asymptotic solutions, and discusses implications for early universe cosmology.

Contribution

It provides the first closed-form solutions for quantum Taub models with matter sources and explores their excited states and asymptotic behaviors.

Findings

Existence of countably infinite excited states.

Multiple asymptotic solutions including wormhole and no boundary types.

Matter sources influence wave function behavior and early universe dynamics.

Abstract

We solve the Wheeler DeWitt equation for the Taub models in closed form when both a cosmological constant and an electromagnetic field are present. In doing so, we examine the 'excited states' of the quantum Taub models with the aforementioned matter sources, and prove the existence of a countably infinite number of 'excited' states. Additionally, we prove the existence of multiple asymptotic solutions to the Lorentzian signature Wheeler DeWitt equation using the Taub analogues of the 'wormhole', and 'no boundary' solutions of its Euclidean-signature Hamilton Jacobi equation; we also study their 'excited states. In the end we investigate qualitatively how our matter sources affect the behavior of our wave functions and argue how these effects within the context of quantum cosmology point to how a primordial electromagnetic field could have played a profound role in the early universe.