Combined analysis of Planck and SPTPol data favors the early dark energy
  models
  We study the implications of the Planck temperature power spectrum at low
multipoles, $\ell<1000$, and SPTPol data. We show that this combination
predicts consistent lensing-induced smoothing of acoustic peaks within
$\Lambda$CDM cosmology and yields the robust predictions of the cosmological
parameters. Combining only the Planck large-scale temperature data and the
SPTPol polarization and lensing measurements within $\Lambda$CDM model we found
substantially lower values of linear matter density perturbation $\sigma_8$
which bring the late-time parameter
$S_8=\sigma_8\sqrt{\Omega_m/0.3}=0.763\pm0.022$ into accordance with galaxy
clustering and weak lensing measurements. It also raises up the Hubble constant
$H_0=69.68\pm1.00{\rm \,\,km\,s^{-1}Mpc^{-1}}$ that reduces the Hubble tension
to the $2.5\sigma$ level. We examine the residual tension in the Early Dark
Energy (EDE) model which produces the brief energy injection prior to
recombination. We implement both the background and perturbation evolutions of
the scalar field which potential scales as $V(\phi)\propto \phi^{2n}$.
Including cosmic shear measurements (KiDS, VIKING-450, DES) and local
distance-ladder data (SH0ES) to the combined fit we found that EDE completely
alleviates the Hubble tension while not degradating the fit to large-scale
structure data. The EDE scenario significantly improves the goodness-of-fit by
$2.9\sigma$ in comparison with the concordance $\Lambda$CDM model. The account
for the intermediate-redshift data (the supernova dataset and baryon acoustic
oscillation data) fits perfectly to our parameter predictions and indicates the
preference of EDE over $\Lambda$CDM at $3\sigma$.
