DEMNUni: ISW, Rees-Sciama, and weak-lensing in the presence of massive neutrinos

We present, for the first time in the literature, a full reconstruction of the total (linear and non-linear) ISW/Rees-Sciama effect in the presence of massive neutrinos, together with its cross-correlations with CMB-lensing and weak-lensing signals. The present analyses make use of all-sky maps extracted via ray-tracing across the gravitational potential distribution provided by the "Dark Energy and Massive Neutrino Universe" (DEMNUni) project, a set of large-volume, high-resolution cosmological N-body simulations, where neutrinos are treated as separate collisionless particles. We correctly recover, at $1-2\%$ accuracy, the linear predictions from CAMB. Concerning the CMB-lensing and weak-lensing signals, we also recover, with similar accuracy, the signal predicted by Boltzmann codes, once non-linear neutrino corrections to Halofit are accounted for. Interestingly, in the ISW/Rees-Sciama signal, and its cross correlation with lensing, we find an excess of power with respect to the massless case, due to free streaming neutrinos, roughly at the transition scale between the linear and non-linear regimes. The excess is $\sim 5-10\%$ at $l\sim 100$ for the ISW/Rees-Sciama auto power spectrum, depending on the total neutrino mass $M_\nu$, and becomes a factor of $\sim 4$ for $M_\nu=0.3$ eV, at $l\sim 600$, for the ISW/Rees-Sciama cross power with CMB-lensing. This effect should be taken into account for the correct estimation of the CMB temperature bispectrum in the presence of massive neutrinos.