The unphysical character of dark energy fluids

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.Comment: 8 pages, 1 figur

Barrow's black hole entropy and the equipartition theorem

The Barrow entropy appears from the fact that the black hole surface can be modified due to quantum gravitational outcome. The measure of this perturbation is given by a new exponent $\Delta$. In this letter we have shown that, from the standard mathematical form of the equipartition theorem, we can relate it with Barrow entropy. From this equivalence, we have calculated precisely the value of the exponent for the equipartition law. After that, we tested the thermodynamical coherence of the system by calculating the heat capacity which established an interval of the possible thermodynamical coherent values of Barrow entropic exponent and corroborated our first result.Comment: minor adjustment