Laboratory experiments measuring neutrino oscillations , indicate small mass differences between different mass eigenstates of neutrinos .
The absolute mass scale is however not determined , with at present the strongest upper limits coming from astronomical observations rather than terrestrial experiments .
The presence of massive neutrinos suppresses the growth of perturbations below a characteristic mass scale , thereby leading to a decreased abundance of collapsed dark matter halos .
Here we show that this effect can significantly alter the predicted luminosity function ( LF ) of high redshift galaxies .
In particular we demonstrate that a stringent constraint on the neutrino mass can be obtained using the well measured galaxy LF and our semi-analytic structure formation models .
Combining the constraints from the Wilkinson Microwave Anisotropy Probe 7 year ( WMAP7 ) data with the LF data at z \sim 4 , we get a limit on the sum of the masses of 3 degenerate neutrinos \Sigma m _ { \nu } < 0.52 eV at the 95 % CL .
The additional constraints using the prior on Hubble constant strengthens this limit to \Sigma m _ { \nu } \leq 0.29 eV at the 95 % CL .
This neutrino mass limit is a factor \sim 4 improvement compared to the constraint based on the WMAP7 data alone , and as stringent as known limits based on other astronomical observations .
As different astronomical measurements may suffer from different set of biases , the method presented here provides a complementary probe of \Sigma m _ { \nu } .
We suggest that repeating this exercise on well measured luminosity functions over different redshift ranges can provide independent and tighter constraints on \Sigma m _ { \nu } .