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 _ { \nu } 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 _ { \nu } 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 _ { \nu } \sim 0.05 eV , we do not expect the ISW-galaxy correlation to be ever sensitive to m _ { \nu } .