Autonomous systems and the dynamics of f(Q,ϕ) gravity: Stability and cosmic acceleration

The cosmological dynamics of [Formula: see text] gravity, where [Formula: see text] represents the non-metricity scalar governing the gravitational interaction and [Formula: see text] is a scalar field, are systematically examined using dynamical systems analysis. By reformulating the gravitational field equations as an autonomous system, the study investigates the late-time evolution of the Universe for various models. The stability of cosmological solutions is assessed through a detailed evaluation of eigenvalues, phase portraits, and the application of center manifold theory to non-hyperbolic critical points. This analysis reveals that [Formula: see text] gravity effectively explains the Universe’s accelerated expansion, with at least one stable node identified in each model. Additionally, the equation of state parameters and density parameters are analyzed across matter-dominated, radiation-dominated, and dark energy phases. Graphical representations of these parameters highlight the models’ capacity to describe key cosmological epochs and their transitions. Overall, the findings demonstrate the potential of symmetric teleparallel-based [Formula: see text] gravity to provide a robust framework for describing late-time cosmic acceleration and other essential features of the Universe’s evolution.