Bose-Einstein condensation of photons in the matter-dominated universe

TL;DR

This paper explores the theoretical possibility of Bose-Einstein condensation of photons in a universe modeled as an ideal white body, revealing how the condensate forms and behaves at different temperatures.

Contribution

It introduces a quantum statistical framework for photon BEC in an ideal white body universe and analyzes the transition temperature and spectral properties.

Findings

Transition temperature increases with photon density.

Condensate fraction decreases from 1 to 0 as temperature rises.

Spectral intensity matches blackbody radiation below T_c.

Abstract

In 1914, Planck introduced the concept of a white body. In nature, no true white bodies are known. We assume that the universe after last-scattering is an ideal white body that contains a tremendously large number of thermal photons and is at an extremely high temperature. Bose-Einstein condensation of photons in an ideal white body is investigated within the framework of quantum statistical mechanism. The computation shows that the transition temperature $T_c$ is a monotonically increasing function of the number density $n$ of photons. At finite temperature, we find that the condensate fraction $N_0(T)/N$ decreases continuously from unity to zero as the temperature increases from zero to the transition temperature $T_c$. Further, we study the radiation properties of an ideal white body. It is found that in the condensation region of $T<T_c$, the spectral intensity $I(\omega,T)$ of white body radiation is identical with Planck's law for blackbody radiation.