Constraining neutrino masses with the integrated-Sachs-Wolfe-galaxy correlation function

Temperature anisotropies in the cosmic microwave background (CMB) are affected by the late integrated Sachs-Wolfe (lISW) effect caused by any time variation of the gravitational potential on linear scales. Dark energy is not the only source of lISW, since massive neutrinos induce a small decay of the potential on small scales during both matter and dark energy domination. In this work, we study the prospect of using the cross correlation between CMB and galaxy-density maps as a tool for constraining the neutrino mass. On the one hand massive neutrinos reduce the cross-correlation spectrum because free-streaming slows down structure formation; on the other hand, they enhance it through their change in the effective linear growth. We show that in the observable range of scales and redshifts, the first effect dominates, but the second one is not negligible. We carry out an error forecast analysis by fitting some mock data inspired by the Planck satellite, Dark Energy Survey (DES) and Large Synoptic Survey Telescope (LSST). The inclusion of the cross correlation data from Planck and LSST increases the sensitivity to the neutrino mass m_ν by 38% (and to the dark energy equation of state w by 83%) with respect to Planck alone. The correlation between Planck and DES brings a far less significant improvement. This method is not potentially as good for detecting m_ν as the measurement of galaxy, cluster, or cosmic shear power spectra, but since it is independent and affected by different systematics, it remains potentially interesting if the total neutrino mass is of the order of 0.2 eV; if instead it is close to the lower bound from atmospheric oscillations, m_ν∼0.05  eV, we do not expect the ISW-galaxy correlation to be ever sensitive to m_ν.