The meso-inflationary QCD axion

We study the possibility that the axion Peccei-Quinn symmetry is spontaneously broken after the beginning of inflation. This scenario interpolates between pre-inflationary and post-inflationary axion cosmology with significant phenomenological differences from both. Since the axion is not present at the early stages of inflation large inflationary fluctuations are produced only at scales not constrained by CMB, avoiding the strongest isocurvature constraints. The energy density in isocurvature perturbations at short scales however can be comparable with the adiabatic contribution from misalignment. These large overdensities can lead to the formation of axion mini-clusters and also to constraints from Lyman-$\alpha$ forest and future CMB spectral distortion measurements. If Peccei-Quinn symmetry is broken during the first O(25) e-foldings of inflation no axions are produced from the string network but contributions from the annihilation of domain walls can further boost the abundance. This scenario is minimally realized if the Hubble scale during inflation drops below the Peccei-Quinn symmetry breaking scale but other realizations are possible.