Galileon versus quintessence: a comparative phase space analysis and late-time cosmic relevance

Abstract We perform a comparative phase space analysis of the light mass Galileon model and standard quintessence in the context of late-time cosmic acceleration. Focusing on a spatially flat FLRW background, we consider a cubic Galileon interaction supplemented by a scalar potential and examine three representative choices of the potential: a generalized cosh potential, a simple cosh potential, and a linear potential. By introducing suitable dimensionless variables, the cosmological field equations are reformulated as an autonomous dynamical system, allowing a systematic investigation of the stationary points and their stability properties. For the light mass Galileon scenario, we find that although the phase space admits scalar field dominated solutions, all critical points are of saddle type for the potentials considered. In particular, no stable late-time accelerating attractor emerges, even in the presence of de-Sitter like configurations. In contrast, the quintessence limit admits stable de-Sitter attractors for cosh potentials, providing a viable description of the observed late-time acceleration. Our results highlight a key qualitative distinction between Galileon and quintessence cosmologies and indicate that, within the light mass Galileon framework, the higher-order Galileon interactions may be required to realize a stable accelerating Universe.