On the Non-Equilibrium Early Universe

We study non--equilibrium ensemble corrections to particle masses and the effective potential in the early universe, using a uniform momentum distribution as an example. The resulting thermalization temperature is computed assuming \sm degrees of freedom, and it is always found to be below $5\times 10^{14}$ GeV, implying that GUT phase transitions typically take place out of equilibrium. For the abelian Higgs model we find that the phase transition is of second order if it occurs before equilibration, in contrast to the first order equilibrium phase transition.