Unified dark energy thermodynamics: varying w and the -1-crossing

TL;DR

This paper presents a comprehensive thermodynamic analysis of dark energy with a variable equation-of-state parameter, demonstrating that the -1-crossing is a smooth crossover, not a phase transition, with well-defined thermodynamic quantities.

Contribution

It provides a unified framework showing all thermodynamic quantities remain regular at the -1-crossing, including negative temperatures in the phantom regime.

Findings

Thermodynamic quantities are well-defined at the -1-crossing.

Temperature is negative in the phantom regime and positive in quintessence.

The -1-crossing is a smooth crossover, not a phase transition.

Abstract

We investigate, in a unified and general way, the thermodynamic properties of dark energy with an arbitrary, varying equation-of-state parameter w(a). We find that all quantities are well defined and regular for every w(a), including at the -1-crossing, with the temperature being negative in the phantom regime (w(a)<-1) and positive in the quintessence one (w(a)>-1). The density and entropy are always positive while the chemical potential can be arbitrary. At the -1-crossing, both temperature and chemical potential are zero. The temperature negativity can only be interpreted in the quantum framework. The regular behavior of all quantities at the -1-crossing, leads to the conclusion that such a crossing does not correspond to a phase transition, but rather to a smooth cross-over.