Cosmological bound on neutrino masses in the light of $H_0$ tension
  Although cosmic microwave background (CMB) is the most powerful cosmological
probe of neutrino masses, it is in trouble with local direct measurements of
$H_0$, which is called the $H_0$ tension. Since neutrino masses are correlated
with $H_0$ in CMB, one can expect the cosmological bound on neutrino masses
would be much affected by the $H_0$ tension. We investigate what impact this
tension brings to cosmological bound on neutrino masses by assuming a model
with modified recombination which has been shown to resolve the tension. We
argue that constraints on neutrino masses become significantly weaker in models
where the $H_0$ tension can be resolved.
