Testing AdS early dark energy with Planck, SPTpol and LSS data
  The Hubble tension might be resolved by injecting a new energy component,
called Early Dark Energy (EDE), prior to recombination. An Anti-de Sitter (AdS)
phase around recombination can make the injected energy decay faster, which
thus allows a higher EDE fraction (so larger $H_0$) while prevents degrading
the CMB fit. In this work, we test the AdS-EDE model with CMB and Large-Scale
Structure (LSS) data. Our CMB dataset consists of low-$\ell$ part of Planck TT
spectrum and SPTpol polarization and lensing measurements, since this dataset
predicts the CMB lensing effect consistent with $\Lambda$CDM expectation.
Combining it with BAO and Pantheon data, we find the bestfit values $H_0=71.92$
km/s/Mpc and $H_0=73.29$ km/s/Mpc without and with the SH0ES prior,
respectively. Including cosmic shear and galaxy clusters data, we have
$H_0=71.87$ km/s/Mpc and $S_8=0.785$, i.e. only $1.3\sigma$ discrepancy with
direct $S_8$ measurement.
