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Following a relativistic heavy ion collision, the quark-gluon plasma producedeventually undergoes a chiral phase transition. We assume that during thisphase 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 actualmomentum cutoff (Landau pole) in the theory at around 1 GeV. Thus it isnecessary to find ways of obtaining a covariantly conserved, renormalizedenergy-momentum tensor when there is a cutoff present (which breakscovariance), in order to identify the effective equation of state of this timeevolving system. We show how to solve this technical problem and then determinethe energy density and pressure of the system as a function of the proper time.We consider different initial conditions and search for instabilities which canlead to the formation of disoriented chiral condensates (DCCs). We find thatthe energy density and pressure both decrease quickly, as is appropriate for arapidly cooling system, and that the energy is numerically conserved.Comment: 15 pages, 5 figures We study the energy density and pressure of an  spherically expanding pion plasma, for both cases, with and without  instabilities. In this last case, we search for the possibility of DCC  formatio

Effective equation of state for a spherically expanding pion plasma