Study of galaxy distributions with SDSS DR14 data and measurement of neutrino masses

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 $\sum m_{\nu }=3m_{\nu }$. Fitting the predictions of the $\mathrm{\Lambda }$CDM model to the Sachs-Wolfe effect, ${\sigma }_8$, the galaxy power spectrum $P_{\text{gal}}(k)$, fluctuations of galaxy counts in spheres of radii ranging from $16\mathrm{/}h$ to $128\mathrm{/}h$ 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} $\text{ (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$n = 1.021 \pm 0.075$\mathrm{.}Thefitalsoreturnsthegalaxybias$b$ including its scale dependence.