Conformally Invariant Cosmology Based on Riemann-Cartan Spacetime

TL;DR

This paper develops a conformally invariant cosmological model based on Riemann-Cartan spacetime, exploring quantum gravitational formalism and wave functions of the universe with specific boundary conditions.

Contribution

It introduces a new conformally invariant GUT-like model incorporating gravity within Riemann-Cartan spacetime and applies quantum cosmology formalism to specific minisuperspace models.

Findings

Wave functions of the universe are computed for de Sitter minisuperspace.

Probability distributions for scalar fields are derived under different boundary conditions.

The model provides a framework for quantum cosmology with conformal invariance.

Abstract

Conformally invariant GUT-like model including gravity based on Riemann - Cartan space-time $U_4$ is considered. Cosmological scenario that follows from the model is discussed and standard quantum gravitational formalism in the Arnowitt-Deser-Misner form is developed. General formalism is then illustrated on Bianchi-IX minisuperspace cosmological model. Wave functions of the universe in the de Sitter minisuperspace model with Vilenkin and Hartle-Hawking boundary conditions are considered and corresponding probability distributions for the scalar field values are calculated.