Some Remarks on Anthropic Approaches to the Strong CP Problem

Abstract: The peculiar value of $\theta$ is a challenge to the notion of an anthropic landscape. We briefly review the possibility that a suitable axion might arise from an anthropic requirement of dark matter. We then consider an alternative suggestion of Kaloper and Terning that $\theta$ might be correlated with the cosmological constant. We note that in a landscape one expects that $\theta$ is determined by the expectation value of one or more axions. We discuss how a discretuum of values of $\theta$ might arise with an energy distribution dominated by QCD, and find the requirements to be quite stringent. Given such a discretuum, we find limited circumstances where small $\theta$ might be selected by anthropic requirements on the cosmological constant.