  Following a relativistic heavy ion collision, the quark-gluon plasma produced
eventually undergoes a chiral phase transition. We assume that during this
phase transition one can describe the dynamics of the system by the linear
$\sigma$ model and that the expansion can be thought of as mostly radial.
Because the $\sigma$ model is an effective field theory there is an actual
momentum cutoff (Landau pole) in the theory at around 1 GeV. Thus it is
necessary to find ways of obtaining a covariantly conserved, renormalized
energy-momentum tensor when there is a cutoff present (which breaks
covariance), in order to identify the effective equation of state of this time
evolving system. We show how to solve this technical problem and then determine
the energy density and pressure of the system as a function of the proper time.
We consider different initial conditions and search for instabilities which can
lead to the formation of disoriented chiral condensates (DCCs). We find that
the energy density and pressure both decrease quickly, as is appropriate for a
rapidly cooling system, and that the energy is numerically conserved.
