Weighing the Neutrinos with the Galaxy Shape-Shape Correlations
  The galaxies form and evolve in the early epochs through the anisotropic
merging process along the primary narrow filaments, in the direction of which
their shapes become elongated and intrinsically aligned. The nonlinear
evolution of the cosmic web broadens the primary filaments, by entangling them
with multiple secondary filaments, which has an effect of reducing the
anisotropy of the merging process and in consequence weakens the galaxy
shape-shape correlations in the later epochs. Assuming that the degree of the
nonlinearity and complexity of the cosmic web depends on the nature of dark
matter, we propose a hypothesis that the galaxy shape-shape correlation
function, $\eta(r)$, may be a powerful complimentary probe of the total
neutrino mass, $M_{\nu}$. Testing this hypothesis against a high resolution
N-body simulation, we show that the $M_{\nu}$-dependence of $\eta(r)$ at $z=0$
is sensitive enough to distinguish between $M_{\nu}=0.0$ eV and $M_{\nu}=0.1$
eV. We also show that the differences in $\eta(r)$ at $r\le 5\,h^{-1}$Mpc
between the models with massless and massive neutrinos cannot be explained by
their differences in the small-scale density powers, $\sigma_{8}$, which
implies that the galaxy shape-shape correlation function has a potential to
break the notorious cosmic degeneracy between $M_{\nu}$ and $\sigma_{8}$.
