Cosmology of rotating axions and their gravitational-wave signatures

I will discuss axion dynamics in the early universe and its phenomenological signatures. I will in particular discuss the rich phenomenology associated with early rotating axions, that arises from the interplayed dynamics between the axion and its partner, the radial mode of the Peccei-Quinn field. This not only opens a vast parameter space where the axion can be naturally dark matter but also offers striking signals in gravitational-wave stochastic backgrounds of primordial origin.