We are interested in a post-inflation QCD axion model that solves the axion quality problem without introducing a cosmological disaster. In a post-inflation axion model, axion domain walls may form at the QCD phase transition and the canonical solution to the quality problem is naively in tension with the cosmological domain wall problem. Post-inflation axion models also face a potential problem from fractionally charged relics; solving this problem often leads to low-energy Landau poles for Standard Model gauge couplings, reintroducing the quality problem. We study several examples, finding that models that solve the quality problem face cosmological problems, and vice versa. This is not a no-go theorem; nonetheless, we argue that it is much more difficult than generally appreciated to find a viable post-inflation QCD axion model. Successful examples may have a nonstandard cosmological history (e.g., multiple types of cosmic axion strings of different tensions), undermining the widespread expectation that the post-inflation QCD axion scenario predicts a unique mass for axion dark matter.
Ankita Budhraja, Juraj Klaric, Johannes Michel