Some Remarks on Anthropic Approaches to the Strong CP Problem

TL;DR

This paper explores anthropic explanations for the small value of the QCD theta parameter, considering axion-based and cosmological constant correlations within a landscape framework, and discusses the conditions under which small theta could be anthropically selected.

Contribution

It analyzes the feasibility of anthropic selection mechanisms for the QCD theta parameter, including axion models and correlations with the cosmological constant, within a landscape scenario.

Findings

A discretuum of theta values can arise with QCD-dominated energy distribution.

Limited conditions allow anthropic selection of small theta based on the cosmological constant.

Stringent requirements are needed for small theta to be favored anthropically.

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.