Distortions of CMB temperature and polarization anisotropy maps caused by gravitational lensing , observable with high angular resolution and sensitivity , can be used to constrain the sterile neutrino mass , offering several advantages against the analysis based on the combination of CMB , LSS and Ly \alpha forest power spectra .
As the gravitational lensing effect depends on the matter distribution , no assumption on light-to-mass bias is required .
In addition , unlike the galaxy clustering and Ly \alpha forest power spectra , the projected gravitational potential power spectrum probes a larger range of angular scales , the non-linear corrections being required only at very small scales . Taking into account the changes in the time-temperature relation of the primordial plasma and the modification of the neutrino thermal potential , we compute the projected gravitational potential power spectrum and its correlation with the temperature in the presence of DM sterile neutrino . We show that the cosmological parameters are generally not biased when DM sterile neutrino is included .
From this analysis we found a lower limit on DM sterile neutrino mass m _ { \nu _ { s } } > 2.08 keV at 95 % CL , consistent with the lower mass limit obtained from the combined analysis of CMB , SDSS 3D power spectrum and SDSS Ly \alpha forest power spectrum ( m _ { \nu _ { s } } > 1.7 keV ) . We conclude that although the information that can be obtained from lensing extraction is rather limited due to the high level of the lensing noise of Planck experiment , weak lensing of CMB offers a valuable alternative to constrain the dark matter sterile neutrino mass .