Some remarks on anthropic approaches to the strong CP problem

Abstract

The peculiar value of θ 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 θ might be correlated with the cosmological constant. We note that in a landscape one expects that θ is determined by the expectation value of one or more axions. We discuss how a discretuum of values of θ might arise with an energy distribution dominated by QCD, and find the requirements to be quite stringent. Given such a discretuum, we find no circumstances where small θ might be selected by anthropic requirements on the cosmological constant.

The landscape of QCD axion models

“…where θ ∈ [0, 2π) is an angular parameter, which is known as the θ vacuum. 5 This vacuum state has the important property of being an eigenstate of the unitary operator of the gauge transformation…”

“…In fact, as long asθ 1%, nuclear physics and Big Bang Nucleosynthesis are practically unaffected [4], so that the valueθ ∼ 10 −10 does not seem to be connected to any 'catastrophic boundary'. See however [5,70], for some attempts to relate the scanning ofθ with that of the cosmological constant.…”

θ -dependence of light nuclei and nucleosynthesis

“…For further discussions related to this issue, see Refs. [10][11][12]. In the present paper we revisit this issue.…”

Indirect signs of the Peccei-Quinn mechanism

“…3. 7 The CKM phase contributes to EDMs at a level significantly below current and expected future experimental sensitivities, and can be neglected.…”