Neutrino Mass Bounds in the era of Tension Cosmology
  The measurements of Cosmic Microwave Background anisotropies made by the
Planck satellite provide extremely tight upper bounds on the total neutrino
mass scale ($\Sigma m_{\nu}<0.26 eV$ at $95\%$ C.L.). However, as recently
discussed in the literature, Planck data show anomalies that could affect this
result. Here we provide new constraints on neutrino masses using the recent and
complementary CMB measurements from the Atacama Cosmology Telescope DR4 and the
South Polar Telescope SPT-3G experiments. We found that both the ACT-DR4 and
SPT-3G data, when combined with WMAP, mildly suggest a neutrino mass with
$\Sigma m_{\nu}=0.68 \pm 0.31$ eV and $\Sigma m_{\nu}=0.46_{-0.36}^{+0.14}$ eV
at $68 \%$ C.L, respectively. Moreover, when CMB lensing from the Planck
experiment is included, the ACT-DR4 data now indicates a neutrino mass above
the two standard deviations, with $\Sigma m_{\nu}=0.60_{-0.50}^{+0.44}$ eV at
$95 \%$, while WMAP+SPT-3G provides a weak upper limit of $\Sigma m_{\nu}<0.37$
eV at $68 \%$ C.L.. Interestingly, these results are consistent with the Planck
CMB+Lensing constraint of $\Sigma m_{\nu} = 0.41_{-0.25}^{+0.17}$ eV at $68 \%$
C.L. when variation in the $A_{\rm lens}$ parameter are considered. We also
show that these indications are still present after the inclusion of BAO or
SN-Ia data in extended cosmologies that are usually considered to solve the
so-called Hubble tension. A combination of ACT-DR4, WMAP, BAO and constraints
on the Hubble constant from the SH0ES collaboration gives $\Sigma
m_{\nu}=0.39^{+0.13}_{-0.25}$ eV at $68 \%$ C.L. in extended cosmologies. We
conclude that a total neutrino mass above the $0.26$ eV limit still provides an
excellent fit to several cosmological data and that future data must be
considered before safely ruling it out.
