On homothetic cosmological dynamics

Abstract

We consider the homogeneous and isotropic cosmological fluid dynamics which is compatible with a homothetic, timelike motion, equivalent to an equation of state $ρ+ 3P = 0$. By splitting the total pressure $P$ into the sum of an equilibrium part $p$ and a non-equilibrium part $Π$, we find that on thermodynamical grounds this split is necessarily given by $p = ρ$ and $Π= - (4/3)ρ$, corresponding to a dissipative stiff (Zel'dovich) fluid.