$T_0$ censorship of early dark energy and AdS vacua
  Present-day temperature $T_0$ of cosmic microwave background has been
precisely measured by the FIRAS experiment. We identify that the early dark
energy (EDE) (non-negligible around matter-radiation equality) scenario can
remain compatible with the FIRAS result, while lifting the Hubble constant
$H_0$. We perform Monte Carlo Markov chain analysis to confirm our
observations. We also present an $\alpha$-attractor Anti-de Sitter (AdS) model
of EDE, in which the AdS depth is consistently varied in the Monte Carlo Markov
chain analysis. We found that our datasets weakly hinted the existence of an
AdS phase near recombination with $H_0\sim 73$km/s/Mpc at 1$\sigma$ region in
the best-fit model.
