Einstein-Gauss-Bonnet-Myrzakulov Gravity from $R + F(T, G)$: Numerical Insights and Torsion-Gauss-Bonnet Dynamics in Weitzenb\"ock Spacetime

TL;DR

This paper explores the Einstein-Gauss-Bonnet-Myrzakulov gravity model, combining curvature, torsion, and Gauss-Bonnet terms, to explain cosmic acceleration and dark energy through theoretical analysis and observational data.

Contribution

It introduces a comprehensive analysis of the EGBMG model's ability to address cosmological challenges, including dark energy evolution and universe expansion, with numerical and dynamical systems insights.

Findings

EGBMG model aligns with observational data on cosmic acceleration

Demonstrates robustness in explaining large-scale structure formation

Provides new theoretical insights into Weitzenböck spacetime dynamics

Abstract

The study of modified gravity models has garnered significant attention because of their potential to provide alternative explanations for cosmological phenomena, such as the accelerated expansion of the universe and the nature of dark energy. One such model, the Einstein-Gauss-Bonnet-Myrzakulov $R + F(T, G)$ gravity (EGBMG), which incorporates the curvature $R$, torsion $T$, and the Gauss-Bonnet term $G$, offers a promising framework to explore the dynamics of the universe and its evolution. This paper delves into the theoretical and observational implications of the EGBMG model, focusing on its ability to address long-standing challenges in cosmology, including the evolution of dark energy and the transition from early-time inflationary behavior to late-time acceleration. We review recent advancements in the model, including its compatibility with observational data and its ability to provide new insights into cosmic acceleration. Through a combination of theoretical models, dynamical systems analysis, and cosmological diagnostics, we demonstrate the robustness of the EGBMG framework in explaining the large-scale structure of the universe and its accelerated expansion. This paper serves as a step toward further exploring the potential of this model to understand the fundamental forces driving Weitzenb$\"{o}$ck spacetime.