Temperature variation in the dark cosmic fluid in the late universe

Abstract

A one-component dark energy fluid model of the late universe is considered [Formula: see text] 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 ([Formula: see text] in the laminar epoch and [Formula: see text] 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 [Formula: see text] in the laminar case when viscosity is included. Assuming that the laminar/turbulent transition takes place at some time [Formula: see text] before the big rip is reached, we then analyze the positive temperature jump experienced by the fluid at [Formula: see text] if [Formula: see text]. 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.