Lee-Wick theories at high temperature

An extension of the standard model, the Lee-Wick standard model, based on ideas of Lee and Wick was recently introduced. It does not contain quadratic divergences in the Higgs mass and hence solves the hierarchy puzzle. The Lee-Wick standard model contains new heavy Lee-Wick resonances at the TeV scale that decay to ordinary particles. In this Letter we examine the behavior of Lee-Wick resonances at high temperature. We argue that they contribute negatively to the energy density ρ and pressure p and at temperatures much greater than their mass M their O(T4) contributions to ρ and p cancel against those of the ordinary (light) particles. The remaining O(M2T2) contributions are positive and result in an equation of state that approaches w=1 from below as T→∞.