Qualitative Stability Analysis of Cosmological Parameters in $f(T,B)$ Gravity

TL;DR

This paper performs a qualitative stability analysis of cosmological solutions in $f(T,B)$ gravity, exploring critical points, stability, and universe behavior for two specific models using dynamical system techniques.

Contribution

It introduces a dynamical system approach to analyze the stability and cosmological implications of two specific $f(T,B)$ gravity models, providing new insights into their phase space and universe evolution.

Findings

Both models have four critical points with stable regions.

The effective equation of state indicates quintessence behavior.

Results align with observational constraints on cosmological parameters.

Abstract

We analyze the cosmological solutions of $f(T,B)$ gravity using dynamical system analysis where $T$ is the torsion scalar and $B$ be the boundary term scalar. In our work, we assume two specific cosmological models. For first model, we consider $ f(T,B)=f_{0}(B^{k}+T^{m})$, where $k$ and $m$ are constants. For second model, we consider $f(T,B)=f_{0}T B$. We generate an autonomous system of differential equations for each models by introducing new dimensionless variables. To solve this system of equations, we use dynamical system analysis. We also investigate the critical points and their natures, stability conditions and their behaviors of Universe expansion. For both models, we get four critical points. The phase plots of this system are analyzed in detail and study their geometrical interpretations also. In both model, we evaluated density parameters such as $\Omega_{r}$, $\Omega_{m}$, $\Omega_{\Lambda}$ and $\omega_{eff}$ and deceleration parameter $(q)$ and find their suitable range of the parameter $\lambda$ for stability. For first model, we get $\omega_{eff}=-0.833,-0.166$ and for second model, we get $\omega_{eff}=-\frac{1}{3}$. This shows that both the models are in quintessence phase. Further, we compare the values of EoS parameter and deceleration parameter with the observational values.