We study galaxy distributions with Sloan Digital Sky Survey SDSS DR14 data and with simulations searching for variables that can constrain neutrino masses .
To be specific , we consider the scenario of three active neutrino eigenstates with approximately the same mass , so \sum m _ { \nu } = 3 m _ { \nu } .
Fitting the predictions of the \Lambda CDM model to the Sachs-Wolfe effect , \sigma _ { 8 } , the galaxy power spectrum P _ { \textrm { gal } } ( k ) , fluctuations of galaxy counts in spheres of radii ranging from 16 / h to 128 / h Mpc , BAO measurements , and h = 0.678 \pm 0.009 , in various combinations , with free spectral index n , and free galaxy bias and galaxy bias slope , we obtain consistent measurements of \sum m _ { \nu } .
The results depend on h , so we have presented confidence contours in the ( \sum m _ { \nu } ,h ) plane .
A global fit with h = 0.678 \pm 0.009 obtains \sum m _ { \nu } = 0.719 \pm 0.312 \textrm { ( stat ) } ^ { +0.055 } _ { -0.028 } \textrm { ( syst ) } eV , and the amplitude and spectral index of the power spectrum of linear density fluctuations P ( k ) : N ^ { 2 } = ( 2.09 \pm 0.33 ) \times 10 ^ { -10 } , and n = 1.021 \pm 0.075 .
The fit also returns the galaxy bias b including its scale dependence .