  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 $z\sim2000$ and ending
shortly after recombination (hereafter the universe will settle down in a
$\Lambda>0$ phase until now), and obtain a best-fit $H_0=72.74$ km/s/Mpc
without degrading the CMB fit compared with the standard $\Lambda$CDM model.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Theory