Power-law dark energy model: Dynamical stability, thermodynamics, and observational signatures

We investigate the cosmological dynamics of a generalized dark energy fluid with a power-law equation of state, [Formula: see text], in a flat FLRW universe. For the regime [Formula: see text], the model features a stable de Sitter attractor at an effective cosmological constant density [Formula: see text], which naturally drives late-time acceleration without fine-tuning. Our background-level dynamical stability analysis shows that this framework, particularly the quadratic case ([Formula: see text]), avoids ghost instabilities while accommodating both phantom ([Formula: see text]) and quintessence behaviors. The Hubble evolution shows asymptotic agreement with [Formula: see text]CDM at high redshifts but features late-time deviations with the potential to alleviate the Hubble tension. Thermodynamically, the generalized second law is satisfied when the null energy condition holds, which occurs naturally for [Formula: see text]. The model’s consistency with fundamental principles and its ability to replicate key observational trends establish it as a compelling alternative to the cosmological constant.