Stability and Thermodynamics of a Generalized Power-Law Dark Energy Model

TL;DR

This paper explores a generalized power-law dark energy model that exhibits stable late-time acceleration, phantom crossing, and thermodynamic consistency, aligning with observations and avoiding instabilities.

Contribution

It introduces a novel dark energy equation of state with a rich phase space, demonstrating stability, phantom crossing, and thermodynamic viability, advancing theoretical understanding of cosmic acceleration.

Findings

The model exhibits a stable attractor with an effective cosmological constant.

It allows phantom crossing without ghost instabilities.

Thermodynamic laws are satisfied under certain conditions.

Abstract

We investigate a generalized power-law dark energy equation of state of the form $p = w\rho - \beta\rho^m$ in a flat FLRW universe, analyzing its dynamical stability and thermodynamic consistency. The model exhibits a rich phase space structure, with an effective cosmological constant $\rho^* = [(1+w)/\beta]^{1/(m-1)}$ emerging as a stable attractor for $(w < -1,~ m > 1)$. Notably, the universe evolves from an early de Sitter phase ($w \to -1$) to a late-time de Sitter-like one with phantom crossing ($w(z) < -1$), aligning with DESI observations. Dynamical analysis reveals that the $m > 1$ regime avoids ghost instabilities while accommodating phantom behavior, with $m = 2$ providing particular theoretical advantages. Thermodynamically, the Generalized Second Law holds when the null energy condition $\rho + p \geq 0$ is satisfied, which naturally occurs for $\rho \geq \rho^*$. The model's compatibility with both observational data and fundamental thermodynamic principles suggests it as a viable framework for describing late-time cosmic acceleration, resolving tensions associated with phantom crossing while maintaining entropy dominance of the cosmological horizon.