Relaxation versus collision times in the cosmological radiative era

TL;DR

This paper investigates the relaxation times of shear viscosity in the early universe's radiative era, showing that they can vastly exceed photon-electron collision times, and highlights limitations of simplified transport equations.

Contribution

It demonstrates that the full EIT transport equation predicts significantly larger shear viscosity relaxation times than the truncated version, affecting decoupling modeling.

Findings

Relaxation time of shear viscosity can be much larger than photon-electron collision time.

Truncated transport equations are inadequate for modeling matter-radiation decoupling.

Full EIT transport equation provides a more accurate description of early universe dynamics.

Abstract

We consider the Lema\^{\i}tre-Tolman-Bondi metric with an inhomogeneous viscous fluid source satisfying the equation of state of an interactive mixture of radiation and matter. Assuming conditions prior to the decoupling era, we apply Extended Irreversible Thermodynamcs (EIT) to this mixture. Using the full transport equation of EIT we show that the relaxation time of shear viscosity can be several orders of magnitude larger than the Thomson collision time between photons and electrons. A comparison with the ``truncated'' transport equation for these models reveals that the latter cannot describe properly the decoupling of matter and radiation