Stability of $f(Q, B)$ Gravity via Dynamical System Approach: a Comprehensive Bayesian Statistical Analysis

In this work, we explore the cosmological stability of $f(Q, B)$ gravity using a dynamical system approach, where $Q$ denotes the nonmetricity scalar and $B$ represents the boundary term. We determine the model parameters of $f(Q, B)$ through Bayesian statistical analysis, employing Markov Chain Monte Carlo techniques. This analysis incorporates numerical solutions and observational data from cosmic chronometers, the extended Pantheon$^+$ data set, and baryonic acoustic oscillation measurements. Our findings reveal a stable critical point within the dynamical system of the model, corresponding to the de Sitter phase, which is consistent with current observations of the Universe dominated by dark energy and undergoing late-time accelerated expansion. Additionally, we utilize Center Manifold Theory to examine the stability of this critical point, providing deeper insights into the behavior of the model. The cosmological implications of $f(Q, B)$ gravity indicate a smooth transition in the deceleration parameters from deceleration to the acceleration phase, underscoring the potential of the model to describe the evolution of the Universe. Our results suggests that the $f(Q, B)$ model presents a viable alternative to the standard $\Lambda$CDM model, effectively capturing the observed acceleration of the Universe and offering a robust framework for explaining the dynamics of cosmic expansion.