IRRATIONAL AXIONS AS A SOLUTION OF THE STRONG CP PROBLEM IN AN ETERNAL UNIVERSE

We exhibit a novel solution of the strong CP problem, which does not involve any massless particles. The low energy effective lagrangian of our model involves a discrete space-time independent axion field which can be thought of as a parameter labeling a dense set of theta-vacua. In the full theory this parameter is seen be dynamical, and the model seeks the state of lowest energy, which has theta(eff) = 0. The processes which mediate transitions between theta-vacua involve heavy degrees of freedom and are very slow. Consquently, we do not know whether our model can solve the strong CP problem in a universe which has been cool for only a finite time. We present several speculations about the cosmological evolution of our model.