Is the Hubble tension a hint of AdS phase around recombination?

Anti-de Sitter (AdS) vacua, being theoretically important, might have an unexpected impact on the observable universe. We find that in early dark energy (EDE) scenarios the existence of AdS vacua around recombination can effectively lift the CMB-inferred $H_0$ value. As an example, we study a phenomenological EDE model with an AdS phase starting at the redshift $z\sim 2000$ and ending shortly after recombination (hereafter the universe will settle down in a $\mathrm{\Lambda }>0$ phase until now), and obtain a best-fit $H_0=72.74$ km/s/Mpc without degrading the CMB fit compared with the standard $\mathrm{\Lambda }$CDM model.