Title: The Stochastic Axiverse

Abstract: I discuss different methods to regulate the overproduction of axions in the axiverse, showing that the minimal requirement to soften this problem is a long period of low-scale inflation. However, in this case, if the inflationary Hubble scale is lower than around O(100) eV, no relic DM axion is produced in the early Universe. Cosmological production of some axions may be activated, via the misalignment mechanism, if their potential minimum changes between inflation and today. As a particular example, I will discuss how the maximal-misalignment mechanism dilutes the effect of dangerous axions and allows the production of axion DM in a controlled way. In this case, the potential of the axion that realises the mechanism shifts by a factor ∆θ = π between the inflationary epoch and today, and the axion starts to oscillate from the top of its potential. I will also show that axions with masses m=O(1-100) H0 realising the maximal-misalignment mechanism generically behave as dark energy with a decay constant that can take values well below the Planck scale, avoiding problems associated to super-Planckian scales.