The unphysical character of dark energy fluids

TL;DR

This paper demonstrates that it is impossible to model dark energy with a differentiable equation of state parameter that satisfies thermodynamic stability and positivity of entropy throughout the universe's history.

Contribution

It proves the unphysical nature of dark energy fluids by showing the non-existence of a suitable differentiable equation of state function over cosmic time.

Findings

No differentiable $w(a)$ can satisfy all thermodynamic conditions for dark energy.

Dark energy models with smooth $w(a)$ are incompatible with thermodynamic stability.

The results challenge the physical viability of certain dark energy fluid models.

Abstract

It is well known that, in the context of general relativity, an unknown kind of matter that must violate the strong energy condition is required to explain the current accelerated phase of expansion of the Universe. This unknown component is called dark energy and is characterized by an equation of state parameter $w=p/\rho<-1/3$. Thermodynamic stability requires that $3w-d\ln |w|/d\ln a\ge0$ and positiveness of entropy that $w\ge-1$. In this paper we proof that we cannot obtain a differentiable function $w(a)$ to represent the dark energy that satisfies these conditions trough the entire history of the Universe.