1 through 4 we show the evolution of the effective potential with increasing temperature for four sets of $\epsilon$. All of these represent a slice through the $V - \sigma$ plane, and are normalized such that $V_{min} = 0$ at each temperature. One can imagine that a system cooling through $T_1$ could get trapped in the metastable minimum. We shall consider such possibilities in the following sections. We call this the [*proximal*]{} chiral phase transition, since it is a consequence of the proximity of exact chiral symmetry in parameter (quark mass) space, but it is not a true phase transition in the thermodynamic sense.

Cosmological Constraints
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Considerations of phase transitions in the early Universe have been very useful in restricting particle theory models. We now ask whether cosmology places any constraints on the parameters characterizing the effective potential in eq. (1). As mentioned earlier, we will be considering only $\epsilon_1$ and $\epsilon_2$ to be non-zero as this is sufficient to capture the qualitative aspects of the effective potential. It is well-known that when the effective potential has more than one disconnected minima then domain walls are produced in a phase transition. For the potential term in eq. (4) this 