Analyzing DGP braneworld model stability through phase space phenomenon

This study explores the cosmological dynamics of the Dvali-Gabadadze-Porrati (DGP) braneworld model, focusing on its behavior under various forms of nonlinear interaction between dark energy and dark matter. Employing a dynamical systems approach, the research identifies critical points in the cosmological evolution and examines their stability under perturbations. Four different interaction models are considered to analyze their effects on the late-time acceleration of the universe. The results reveal that certain interaction terms can lead to stable, accelerating solutions that are consistent with observational data. The study highlights how specific nonlinear interactions can influence cosmic evolution and provide viable alternatives to the standard ΛCDM model. These findings contribute to a deeper understanding of modified gravity scenarios and their role in addressing dark energy challenges.