On Effective Degrees of Freedom in the Early Universe

TL;DR

This paper analyzes the effective degrees of freedom in the early universe across different particle species and phases, including transitions from quark-gluon plasma to hadron gas, to better understand the thermodynamic evolution shortly after the Big Bang.

Contribution

It introduces effective degrees of freedom for number density and examines their behavior during key phase transitions in the early universe.

Findings

Effective degrees of freedom vary with temperature and particle species.

Identified crossover temperature of 214 MeV for quark-gluon plasma to hadron gas transition.

Analyzed impact on pressure and entropy during particle annihilation and phase changes.

Abstract

We explore the effective degrees of freedom in the early universe, from before the electroweak scale at a few femtoseconds after the Big Bang, until the last positrons disappeared a few minutes later. We first look at the established concepts of effective degrees of freedom for energy density, pressure and entropy density, and introduce effective degrees of freedom for number density as well. We discuss what happens with particle species as their temperature cools down from relativistic to semi- and non-relativistic temperatures, and then annihilates completely. This will affect the pressure as well as the entropy per particle. We also look at the transition from a quark-gluon plasma to a hadron gas. Using a list of known hadrons, we use a "cross-over" temperature of 214 MeV where the effective degrees of freedom for a quark-gluon plasma equals that of a hadron gas.