On Noether approach in the cosmological model with scalar and gauge fields: symmetries and the selection rule

TL;DR

This paper explores the application of Noether symmetries in a cosmological model with scalar and gauge fields, analyzing quantum and classical aspects to understand universe selection.

Contribution

It provides a detailed analysis of Noether symmetries and Lie algebra in a specific quantum cosmological model, strengthening the selection rule for classical universes.

Findings

Correct identification of Noether symmetries and Lie algebra.

Derivation of the Wheeler-De Witt equation and classical trajectories.

Wave function oscillations support the Hartle criterion and universe selection.

Abstract

In this paper, based on the works of Capozziello et al., we have studied the Noether symmetry approach in the cosmological model with scalar and gauge fields proposed recently by Soda et al. The correct Noether symmetries and related Lie algebra are given according to the minisuperspace quantum cosmological model. The Wheeler-De Witt (WDW) equation is presented after quantization and the classical trajectories are then obtained in the semi-classical limit. The oscillating features of the wave function in the cosmic evolution recover the so-called Hartle criterion, and the selection rule in minisuperspace quantum cosmology is strengthened. Then we have realized now the proposition that Noether symmetries select classical universes.