Phase Transitions in an Expanding Universe: Paul Roman’s Models and Some Remarks on Entropy

Abstract

The question of how photon condensation could emerge in an expanding universe is a central issue. Assuming that the formula for the transition temperature T _c which has been derived in the preceding contribution [1],

$${\left( {k{T_c}} \right)^3} = \frac{3}{8}\cdot \frac{{{\pi ^2}}}{{\zeta \left( 3 \right)}}\cdot \frac{{{\hbar ^2}{c^4}}}{{\kappa R}}$$

was valid at any time we would have the following possibilities:

• 1. kT _c varies with R (even if moderately) which means that in the past of our universe the transition temperature was higher than it is now. If there was a correlation between T _c and the hadron masses these masses would have changed in time.

• 2. kT _c is constant which means that at least one natural constant, c, ħ, or κ, changes in the course of the history of the universe. It is unlikely that observational evidence supports such variations in time.

• 3. In a more general theory (L. Castell, private communication) 1 / R is replaced by ((Ṙ/c)² + k) / R. For R = γt ²/4 + c ² k/γ, T _c is constant.