Landscaping the Strong CP Problem

TL;DR

The paper proposes a landscape-based solution to the strong CP problem, suggesting that vacuum energy variations and membrane nucleation can naturally suppress the CP-violating parameter without requiring a light axion.

Contribution

It introduces a novel anthropic landscape mechanism where vacuum energy scanning helps solve the strong CP problem without an axion.

Findings

Vacuum energy variation can assist in solving the strong CP problem.

Parameter space for vacuum energy step size is significantly expanded.

The scenario can suppress the CP-violating parameter below observational limits.

Abstract

One often hears that the strong $CP$ problem is the one problem which cannot be solved by anthropic reasoning. We argue that this is not so. Due to nonperturbative dynamics, states with a different $CP$ violating paramenter $\theta$ acquire different vacuum energies after the QCD phase transition. These add to the total variation of the cosmological constant in the putative landscape of Universes. An interesting possibility arises when the cosmological constant is mostly cancelled by the membrane nucleation mechanism. If the step size in the resulting discretuum of cosmological constants, $\Delta \Lambda$, is in the interval $({\rm meV})^4 < \Delta \Lambda < (100 \, {\rm MeV})^4$, the cancellation of vacuum energy can be assisted by the scanning of $\theta$. For $({\rm meV})^4 < \Delta \Lambda < ({\rm keV})^4$ this yields $\theta < 10^{-10}$, meeting the observational limits. This scenario opens up 24 orders of magnitude of acceptable parameter space for $\Delta \Lambda$ compared to membrane nucleation acting alone. In such a Universe one may not need a light axion to solve the strong $CP$ problem.