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