Supersymmetric Homogeneous Quantum Cosmologies Coupled to a Scalar Field

TL;DR

This paper extends supersymmetric quantum cosmology models to various Bianchi types and special cases, providing explicit solutions to the Wheeler DeWitt equation, including interpretations related to wormholes and no-boundary states.

Contribution

It offers a general framework for homogeneous quantum cosmologies with solvable momentum constraints across multiple Bianchi types and provides new explicit solutions to the Wheeler DeWitt equation.

Findings

Explicit solutions for Bianchi types I, II, VII, VIII, IX.

Identification of solutions with wormhole fluctuations and no-boundary states.

Extension of supersymmetric models to broader cosmological settings.

Abstract

Recent work on $N=2$ supersymmetric Bianchi type IX cosmologies coupled to a scalar field is extended to a general treatment of homogeneous quantum cosmologies with explicitely solvable momentum constraints, i.e. Bianchi types I, II, VII, VIII besides the Bianchi type IX, and special cases, namely the Friedmann universes, the Kantowski-Sachs space, and Taub-NUT space. Besides the earlier explicit solution of the Wheeler DeWitt equation for Bianchi type IX, describing a virtual wormhole fluctuation, an additional explicit solution is given and identified with the `no-boundary state'.