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 $3\sigma$.