The Quality/Cosmology Tension for a Post-Inflation QCD Axion

Post-inflationary QCD axion is an attractive solution to the Strong CP problem because of the possibility to uniquely predict the axion mass if axion makes up all of dark matter. On the other hand, QCD axion models often suffer from the so-called axion quality problem, where the axion shift symmetry is unprotected from quantum gravity effects. In this talk I will discuss the tension between solutions to the quality problem and viable cosmology for post-inflationary QCD axions. I will first discuss in detail a simple Z_N solution as an illustrative example of the close connection between the quality problem and the domain wall problem, and highlight subtleties about the domain wall problem that has been overlooked in the literature. I will then analyze proposals in the literature that involve more complex symmetry structure and show that they share a set of cosmological issues, including the domain wall problem and fractionally charged particles. Our study suggests that a viable post-inflationary QCD axion model is likely to have non-standard cosmological history unlike what is being assumed in recent simulations, and the “correct” axion mass to produce all of dark matter is far from certain.