Temperature Variation in the Dark Cosmic Fluid in the Late Universe

TL;DR

This paper models the temperature evolution of a dark energy fluid transitioning from laminar to turbulent flow in the late universe, deriving new formulas and analyzing temperature and entropy changes at the transition.

Contribution

It introduces a novel formula for the temperature evolution of a viscous dark fluid during the laminar phase and analyzes the effects of turbulence transition on temperature and entropy.

Findings

Temperature increases at turbulence transition if viscosity is higher in turbulence

Derived a new formula for temperature dependence in viscous dark fluid

Identified an analogy between cosmic fluid and Maxwell viscoelastic fluid

Abstract

A one-component dark energy fluid model of the late universe is considered ($w<-1$) when the fluid, initially assumed laminar, makes a transition into a turbulent state of motion. Spatial isotropy is assumed so that only the bulk viscosities are included ($\zeta$ in the laminar epoch and $\zeta_{\rm turb}$ in the turbulent epoch). Both viscosities are assumed to be constants. We derive a formula, new as far as we know, for the time dependence of the temperature $T(t)$ in the laminar case when viscosity is included. Assuming that the laminar/turbulent transition takes place at some time $t_s$ before the big rip is reached, we then analyze the positive temperature jump experienced by the fluid at $t=t_*$ if $\zeta_{\rm turb} > \zeta$. This is just as one would expect physically. The corresponding entropy production is also considered. A special point emphasized in the paper is the analogy that exists between the cosmic fluid and a so-called Maxwell fluid in viscoelasticity.