  We investigate the impact of prior models on the upper bound of the sum of
neutrino masses, $\sum m_{\nu}$. 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 $\sum m_{\nu} \lesssim 0.26$ eV ($95\%$ CI) and yields a strong competitive
upper bound for the lightest neutrino mass species, $m_0^{\nu} < 0.086$ eV
($95\%$ CI). By contrast one of the approximations, which is somewhat
inconsistent with oscillation experiments, yields an upper bound of $\sum
m_{\nu} \lesssim 0.15$ 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.
