Exploring $\Lambda$CDM extensions with SPT-3G and Planck data: 4$\sigma$
  evidence for neutrino masses, full resolution of the Hubble crisis by dark
  energy with phantom crossing, and all that
  We present new cosmological constraints in a set of motivated extensions of
the $\Lambda$CDM model using the polarization and gravitational lensing
measurements from the South Polar Telescope and the Planck CMB temperature
observations at large angular scales. It was shown in Ref.
\cite{Chudaykin:2020acu} that this CMB setup is free from the Planck anomalies
which could affect the cosmological inference in extended models. Combining the
SPT-3G, SPTPol and Planck large-scale temperature data with the latest
full-shape BOSS and BAO measurements and information from the weak lensing
surveys we find a $4\sigma$ evidence for nonzero neutrino mass, $\sum
m_\nu=0.23\pm0.06$ eV. In $\rm \Lambda$CDM+$N_{\rm eff}$ scenario we
demonstrate that the Planck anomalies do not propagate into cosmological
constraints. Then we examine two promising scenarios with modified late-time
cosmology: one introduces a phantom crossing in dark energy equation of state,
another provides with a sharp transition in the dark energy evolution. We find
that the scenario with a phantom crossing completely alleviate the cosmological
tensions yielding $H_0=73.92\pm1.09{\rm \,\,km\,s^{-1}Mpc^{-1}}$ and
$S_8=0.774\pm0.010$. The Bayesian approach indicates that the model with
phantom crossing is favoured by data as compared to $\Lambda$CDM. For the
transitional dark energy we find no strong evidence for a rapid change in its
equation of state after including the BAO from the BOSS DR12. Our
proof-of-concept analysis shows that the Planck anomalies severely obscure the
cosmological inference in some extensions of the $\Lambda$CDM model. More
precise CMB data is needed to validate our conclusions on neutrino masses and
phantom crossing in the dark energy sector.
