Axion-CMB scenario in a supercooled universe

Axion-CMB scenario is an interesting possibility to explain the temperature anisotropy of cosmic microwave background (CMB) by primordial fluctuations QCD axion \cite{Iso:2020pzv}. In this scenario, radiations are generated energy exchange between axions and radiations, which results in correlation CMB anisotropies. Consequently, cosmological observations stringently constrain a model early history universe. particular, we need large fraction $\Omega_A^{}$ at phase transition, but it must become tiny present universe suppress isocurvature power spectrum. One natural scenarios realize such situation thermal inflation can sufficiently dilute abundance. Thermal occurs various models. paper, focus on classically conformal (CC) $B$-$L$ with axion. model, undergoes long supercooling era electroweak symmetries, naturally occurs. Thus be good candidate for axion-CMB scenario. But abundance transition shown insufficient original CC model. To overcome situation, extend introducing $N$ scalar fields $S$ (either massive or massless) consider novel that $O(N)$ sectors evolve almost separately We find all necessary conditions satisfied some parameter regions massless fields, typically $N\sim 10^{19}$ mass gauge boson around $5-10$ TeV.