Light mass Galileon: Phase space analysis and its late time cosmic relevance

We investigate the Galileon scalar field model by considering the lowest order Galileon term in the Lagrangian, ( ∂ μ ϕ ) 2 □ ϕ through the introduction of a field potential. We explore the late-time cosmological development of light mass Galileon utilizing two different forms for V ( ϕ ) , specifically the double exponential and Quintessence-Driven Slow-Contraction CDM potentials. We identify the critical points and assess their stability for these models. Our findings indicate that the light mass Galileon with double exponential potential facilitates the attainment of a stable attractor solution, while a stable solution is unattainable in the scenario of light mass Galileon with Quintessence-Driven Slow-Contraction CDM potential. Furthermore, in the former case, we derive a phase portrait in which all trajectories converge towards the stable attractor point.