  We study whether non-linear gravitational effects of relic neutrinos on the
development of clustering and large-scale structure may be observable by weak
gravitational lensing. We compute the density profile of relic massive
neutrinos in a spherical model of a cluster of galaxies, for several neutrino
mass schemes and cluster masses. Relic neutrinos add a small perturbation to
the mass profile, making it more extended in the outer parts. In principle,
this non-linear neutrino perturbation is detectable in an all-sky weak lensing
survey such as EUCLID by averaging the shear profile of a large fraction of the
visible massive clusters in the universe, or from its signature in the general
weak lensing power spectrum or its cross-spectrum with galaxies. However,
correctly modeling the distribution of mass in baryons and cold dark matter and
suppressing any systematic errors to the accuracy required for detecting this
neutrino perturbation is severely challenging.
