Landscaping the strong CP problem

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 θ 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, ΔΛ, is in the interval (meV)⁴< ΔΛ < (100 MeV)⁴, the cancellation of vacuum energy can be assisted by the scanning of θ. For (meV)⁴< ΔΛ < (keV)⁴ this may yield θ < 10⁻¹⁰, meeting the observational limits. This scenario opens up 24 orders of magnitude of acceptable parameter space for ΔΛ compared to membrane nucleation acting alone. In such a Universe one may not need a light axion to solve the strong CP problem.