On homothetic cosmological dynamics

TL;DR

This paper explores a specific cosmological fluid model with homothetic symmetry, revealing that thermodynamics constrains it to a dissipative stiff fluid with particular pressure components.

Contribution

It introduces a novel analysis of homothetic cosmological fluids, showing the pressure split must follow thermodynamic principles, leading to a specific dissipative fluid model.

Findings

The pressure split is constrained to p = ρ and Π = -(4/3)ρ.

The model corresponds to a dissipative stiff (Zel'dovich) fluid.

Homothetic symmetry implies specific thermodynamic conditions.

Abstract

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