Weighing neutrinos: weak lensing approach

We study the possibility for a measurement of neutrino mass using weak grav itational lensing. The presence of non-zero mass neutrinos leads to a suppr ession of power at small scales and reduces the expected weak lensing signa l. The measurement of such a suppression in the weak lensing power spectrum allows a direct measurement of the neutrino mass, in contrast to various o ther experiments which only allow mass splittings between two neutrino spec ies. Making reasonable assumptions on the accuracy of cosmological paramete rs, we suggest that a weak lensing survey of 100 sqr. degrees can be easily used to detect neutrinos down to a mass limit of similar to 3.5 eV at the 2 sigma level. This limit is lower than current limits on neutrino mass, su ch as from the Ly alpha forest and SN1987A. An ultimate weak lensing survey of pi steradians down to a magnitude limit of 25 can be used to detect neu trinos down to a mass limit of 0.4 eV at the 2 sigma level, provided that o ther cosmological parameters will be known to an accuracy expected from cos mic microwave background spectrum using the MAP satellite. With improved pa rameters estimated from the PLANCK satellite, the limit on neutrino mass fr om weak lensing can be further lowered by another factor of 3 to 4. For muc h smaller surveys (similar to 10 sqr. degrees) that are likely to be first available in the near future with several wide-field cameras, the presence of neutrinos can be safely ignored when deriving conventional cosmological parameters such as the mass density of the Universe. However, armed with co smological parameter estimates with other techniques, even such small area surveys allow a strong possibility to investigate the presence of non-zero mass neutrinos.