Late-time-accelerated expansion arisen from gauge fields in an anisotropic background and a fruitful trick for Noether's approach

TL;DR

This paper introduces a novel CSSS-trick approach to find analytical solutions in anisotropic modified teleparallel gravity, revealing late-time acceleration, dark matter potential, and aligning with observational data.

Contribution

The paper proposes the CSSS-trick method to obtain solutions with more conserved currents, enhancing the Noether symmetry approach in anisotropic gravity models.

Findings

Unified dark matter potential derived from gauge fields.

Solutions align with recent observational data.

Wave function oscillations recover Hartle's criterion.

Abstract

In this paper, a modified teleparallel gravity action containing a coupling between a scalar field potential and magnetism, in anisotropic and homogeneous backgrounds, is investigated through Noether symmetry approach. The focus of this work is to describe late-time-accelerated expansion. Since finding analytical solutions carrying all conserved currents emerged by Noether symmetry approach, is very difficult, hence regularly in the literature, the authors split the total symmetry into sub-symmetries and then select, usually, some of them to be carried by the solutions. This manner limits the forms of unknown functions obtained. However, in ref. [68], B.N.S. approach was proposed in order to solve such problems but its main motivation was carrying more conserved currents by solutions. In this paper, by eliminating the aforementioned limitation as much as possible, a trick leading to some graceful forms of unknown functions is suggested. Through this fruitful approach, the solutions may carry more conserved currents than usual ways and maybe new forms of symmetries. I named this new approach to be CSSS-trick (Combination of Sub-symmetries through Special Selections). With this approach, it is demonstrated that the unified dark matter potential is deduced by the gauge fields. Utilizing the $\mathfrak{B}\text{-function}$ method, a detailed data analysis of results obtained yielding perfect agreements with recent observational data are performed. And finally, the Wheeler-De Witt (WDW) equation is discussed to demonstrate recovering the Hartle criterion due to the oscillating feature of the wave function of the universe.