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.