QCD axion bubbles in the presence of ALP resonant conversion

The QCD axion bubbles can form due to an explicit breaking of the Peccei-Quinn symmetry in the early Universe. In this paper, we investigate the modified formation of QCD axion bubble in the presence of axionlike particle (ALP), considering its resonant conversion to QCD axion. We consider a general scenario where the QCD axion mixes with ALP before the QCD phase transition. In this scenario, the energy density of the ALP can be adiabatic transferred to the QCD axion at a temperature $T_R$, resulting in the suppression of the cosmic background temperature $T_B$ at which the energy density of the QCD axion equals that of the radiation. The QCD axion bubbles form when the QCD axions arise during the QCD phase transition. Finally, we briefly discuss the impact of the formation of QCD axion bubbles on the formation of primordial black holes.