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 $\theta$ 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2017
 arXiv:
 arXiv:1710.01740
 Bibcode:
 2017arXiv171001740K
 Keywords:

 High Energy Physics  Theory;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology
 EPrint:
 8 pages, added discussion of expectation value of theta and references