Entropy Production in a Lepton-Photon Universe

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$σ$/d$T$) goes as $T^{-8}$, with the total entropy ($Δσ$) increasing as $T^{-7}$. These rates go slightly down just before the neutrinos decouple, where $Δσ\propto T^{-6.2}$.