Origin of cosmological temperature

TL;DR

This paper proposes a classical solution within the Standard Model and General Relativity that explains the origin of cosmological temperature through an elliptic function, linking universe expansion, gauge fields, and electroweak transition.

Contribution

It introduces a novel elliptic function solution that describes a symmetric universe's expansion and the emergence of temperature without requiring physics beyond the Standard Model.

Findings

The solution predicts a universal temperature at electroweak transition of 28.8 GeV.

The universe's expansion is described by an elliptic function with specific symmetry properties.

The temperature at electroweak transition is independent of the free parameter a_EW.

Abstract

A classical solution of the Standard Model + General Relativity is given by an elliptic function whose periodicity in imaginary time is the origin of cosmological temperature. Nothing beyond the Standard Model is assumed. The solution is a $\mathrm{Spin}(4)$-symmetric universe expanding prior to the electroweak transition. A rapidly oscillating $\mathrm{SU}(2)$ gauge field holds the Higgs field to $0$ with strength inversely proportional to the scale factor $a$. When $a$ reaches $a_{\scriptscriptstyle\mathrm{EW}}$ the solution becomes unstable and the electoweak transition begins. $a_{\scriptscriptstyle\mathrm{EW}}$ is the only free parameter in the solution. The temperature at $a_{\scriptscriptstyle\mathrm{EW}}$ is $m_{H}/{(6\pi)^{1/2}} = 28.8\,\text{GeV} = 3.34 \times 10^{14}\, \text{K}$ whatever the value of $a_{\scriptscriptstyle\mathrm{EW}}$.