We investigate the impact of prior models on the upper bound of the sum of neutrino masses, $sum m_{ u}$. We use data from Large Scale Structure of galaxies, Cosmic Microwave Background, Type Ia SuperNovae, and Big Bang Nucleosynthesis. We probe physically motivated neutrino mass models (respecting oscillation experiment constraints) and compare them to constraints using standard cosmological approximations. The former give a consistent upper bound of $sum m_{ u} lesssim 0.26$ eV ($95%$ CI) and yields a strong competitive upper bound for the lightest neutrino mass species, $m_0^{ u} < 0.086$ eV ($95%$ CI). By contrast one of the approximations, which is somewhat inconsistent with oscillation experiments, yields an upper bound of $sum m_{ u} lesssim 0.15$ eV ($95%$ CI), which differs substantially from the former upper bound. We, therefore, argue that cosmological neutrino mass and hierarchy determination should be pursued using physically motivated models since approximations might lead to incorrect and nonphysical upper bounds.
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