We investigate the impact of prior models on the upper bound of the sum of neutrino masses , \sum m _ { \nu } .
Using data from large scale structure of galaxies , cosmic microwave background , type Ia supernovae , and big bang nucleosynthesis , we argue that cosmological neutrino mass and hierarchy determination should be pursued using exact models , since approximations might lead to incorrect and nonphysical bounds .
We compare constraints from physically motivated neutrino mass models ( i.e. , ones respecting oscillation experiments ) to those from models using standard cosmological approximations .
The former give a consistent upper bound of \sum m _ { \nu } \lesssim 0.26 eV ( 95 % CI ) and yield the first approximation-independent upper bound for the lightest neutrino mass species , m _ { 0 } ^ { \nu } < 0.086 eV ( 95 % CI ) .
By contrast , one of the approximations , which is inconsistent with the known lower bounds from oscillation experiments , yields an upper bound of \sum m _ { \nu } \lesssim 0.15 eV ( 95 % CI ) ; this differs substantially from the physically motivated upper bound .