Irrational Axions as a Solution of The Strong CP Problem in an Eternal Universe

TL;DR

The paper proposes a novel solution to the strong CP problem using an irrational axion field that dynamically relaxes to zero, avoiding massless particles and involving slow vacuum transitions, with cosmological implications.

Contribution

It introduces a new axion-based model that solves the strong CP problem without massless particles and explores its cosmological evolution.

Findings

The model achieves a dynamical relaxation to zero theta parameter.

Transitions between vacua involve heavy, slow processes.

Implications for the universe's evolution and CP violation are discussed.

Abstract

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 spacetime 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 to 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. Consequently, 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.