Alleviating both $H_0$ and $S_8$ tensions: early dark energy lifts the CMB-lockdown on ultralight axion

The existence of ultralight axion (ULA) with mass $\mathcal{O}( 10^{-26}\text{eV})$ is not favored by the CMB observations in the standard $\Lambda$CDM model. We show that the inclusion of early dark energy (EDE) will lift the CMB-lockdown on such ULA, and possibly other forms of dark matter beyond cold dark matter. By performing Monte Carlo Markov Chain analysis, it is found that, as opposed to $\Lambda$CDM, the AdS-EDE cosmology (with an Anti-de Sitter phase around recombination) now allows the existence of axion with mass $10^{-26}$ eV and predicts $6\%$ of the matter in our Universe to be such ULA, which can also help alleviating the $S_8$ tension in EDE.