Entropy Production in a Lepton-Photon Universe

TL;DR

This paper models entropy production during the lepton era of the early Universe using relativistic kinetic theory, finding minimal entropy increase and analyzing temperature-dependent viscosity effects.

Contribution

It introduces a model focusing solely on leptons and photons with temperature-dependent bulk viscosity to quantify entropy production in the early Universe.

Findings

Entropy increases by about 0.071% at neutrino decoupling.

Entropy production rate scales as T^{-8} at high temperatures.

Entropy increase just before decoupling follows T^{-6.2}.

Abstract

We look at the entropy production during the lepton era in the early Universe by using a model where we exclude all particles except the leptons and photons. We assume a temperature dependent viscosity as calculated recently by one of us (Husdal 2016) with use of relativistic kinetic theory. We consider only the bulk viscosity, the shear viscosity being omitted because of spatial isotropy. The rate of entropy production is highest just before the neutrinos decouple. Our results show that the increase in entropy during the lepton era is quite small, about 0.071 % at a decoupling temperature of $T=10^{10}~\mathrm{K}$. This result is slightly smaller than that obtained earlier by Caderni and Fabbri (1977). After the neutrino decoupling, when the Universe has entered the photon era, kinetic-theory arguments no longer support the appearance of a bulk viscosity. At high temperatures and a stable particle ratio, entropy production (d$\sigma$/d$T$) goes as $T^{-8}$, with the total entropy ($\Delta \sigma$) increasing as $T^{-7}$. These rates go slightly down just before the neutrinos decouple, where $\Delta \sigma \propto T^{-6.2}$.