Pre-big bang scenario and the WZW model

TL;DR

This paper explores the use of the WZW model on SU(2) to improve pre-big bang cosmological solutions, successfully addressing some previous difficulties and explaining the observed acceleration of the universe's expansion through the dilation field.

Contribution

It demonstrates that applying the WZW model on SU(2) simplifies the determination of pre- and post-big bang solutions and aligns them with observed cosmic acceleration.

Findings

WZW model on SU(2) reduces solution complexities.

Realistic universe evolution solutions are obtained.

Explains cosmic acceleration via the dilation field.

Abstract

Extensive studies of pre-big bang scenarios for Bianchi-I type universe have been made, at various approximation levels. Knowing the solution of the equations for the post-big bang universe, the symmetries of the equations (time reversal and scale dual transformations) allow the study of pre-big bang solutions. However, the proposed solutions are unable to explain the actually observed acceleration of the expantion of the universe.Calculating the $\beta $ equations for the Non-Linear Sigma model, at the first loop approximation and imposing conformal invariance at this level, lead to equations of motion that simply state that the curvature must be nil, which in turn allows the utilization of groups to solve the $\beta $ equations. This is what is done in the Weiss-Zumino-Witten (WZW) model. In this article, I will show that using the WZW model on $SU_2$, some of the difficulties encountered in the determination of the pre and post big-bang solutions are eliminated. Combining the general results obtained with the $\Lambda $CDM parameters lead to realistic solutions for the evolution of the universe, giving an explanation to the actually observed acceleration of the expansion in terms ot the dilation field $\phi $(t).