Axion dark matter with explicit Peccei-Quinn symmetry breaking in the axiverse

It was shown that the required high quality of the Peccei-Quinn (PQ) symmetry can be a natural outcome of the multiple QCD axions model. In the axiverse, a hypothetical mass mixing between the QCD axions and axion-like particles (ALPs) can occur, which leads to an interesting phenomenon called the level crossing. In this paper, we investigate this mass mixing between one QCD axion and one ALP with the explicit PQ symmetry breaking in the early Universe. The dynamics of the axions and their cosmological evolutions when the level crossing occurs in this scenario are studied in detail. We show the evolution of the mass eigenvalues and the mass mixing angle. Then we check the condition for energy adiabatic transition with the corresponding parameter set. Finally, we estimate the relic density of the QCD axion and ALP dark matter through the misalignment mechanism. We find that, the QCD axion relic density can be suppressed, while the ALP relic density can be enhanced. The level crossing in our scenario may have some cosmological implications, such as the axion domain walls formation, the nano-Hertz gravitational waves emission, and also the primordial black holes formation.