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 anal
ysis based on the combination of CMB, LSS and Lyalpha 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 Lyalpha 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_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 Lyalpha forest power spectrum ($m_{ u_s}>1.7$ 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.
