Solid matter with zero shear modulus in flat universe

TL;DR

This paper investigates solid matter models with zero shear modulus in a flat universe, revealing conditions under which their stress-energy properties mimic radiation or dark energy, and analyzing their perturbations.

Contribution

It introduces solid matter models with zero shear modulus that behave like radiation or dark energy, expanding the understanding of stress-energy tensor properties in cosmology.

Findings

Solid matter with zero shear modulus can mimic radiation and dark energy.

Coordinate independence of certain stress-energy ratios is limited to specific w values.

Second order perturbation equations for these models are derived.

Abstract

For a perfect fluid, the quantity defined through mixed components of the stress-energy tensor $\widetilde{w}=(T_{i}^{\phantom{i}i}/3)/(-T_{0}^{\phantom{0}0})$ is independent on the choice of coordinates only for two values of the pressure to energy density ratio $w=p/\rho$: for radiation with $w=1/3$, and for dark energy with $w=-1$. With other choices of $w$, the quantity $\widetilde{w}$ is coordinate dependent, and $\widetilde{w}=w$ only in the local rest frame of the fluid. We show that the same is true also for solid matter with shear stress Lam\'e coefficient set to zero in a flat Friedmann--Lema\^itre--Robertson--Walker universe with perturbed metric as well as stress-energy tensor. We call the two different solids with coordinate independent $\widetilde{w}$ radiation-like solid and dark energy-like solid, and we restrict ourselves to these two special cases. By analysing second order perturbations we discover two one parametric sets of such solid matter models containing special cases of radiation and dark energy as perfect fluids. We also study equations for perturbations up to the second order for both sets of models.