Viscosity in a Lepton-Photon Universe

TL;DR

This paper investigates the viscosity properties of a lepton-photon universe during the early universe's high-temperature phase, focusing on how particle annihilation affects shear and bulk viscosity, especially with the inclusion of muons and taus.

Contribution

It extends existing models of viscosity in a lepton-photon universe by including muons and taus, showing significant increases in bulk viscosity at high temperatures.

Findings

Bulk viscosity increases by a factor of 100 million with muons included.

Viscosity behavior is significantly affected during particle annihilation periods.

The model replicates previous results and extends them to additional leptons.

Abstract

We look at viscosity production in a universe consisting purely of leptons and photons. This is quite close to what the Universe actually look like when the temperature was between $10^{10}$ K and $10^{12}$ K ($1$ -- $100$ MeV). By taking the strong force and the hadronic particles out of the equation, we can examine how the viscous forces behave with all the 12 leptons present. By this we study how shear- and (more interestingly) bulk viscosity is affected during periods with particle annihilation. We use the theory given by Hoogeveen et. al. from 1986, replicate their 9-particle results and expanded it to include the muon and tau particles as well. This will impact the bulk viscosity immensely for high temperatures. We will show that during the beginning of the lepton era, when the temperature is around 100 MeV, the bulk viscosity will be roughly 100 million times larger with muons included in the model compared to a model without.