The combination of current large scale structure and cosmic microwave background ( CMB ) anisotropies data can place strong constraints on the sum of the neutrino masses .
Here we show that future cosmic shear experiments , in combination with CMB constraints , can provide the statistical accuracy required to answer questions about differences in the mass of individual neutrino species .
Allowing for the possibility that masses are non-degenerate we combine Fisher matrix forecasts for a weak lensing survey like Euclid with those for the forthcoming Planck experiment .
Under the assumption that neutrino mass splitting is described by a normal hierarchy we find that the combination Planck and Euclid will possibly reach enough sensitivity to put a constraint on the mass of a single species .
Using a Bayesian evidence calculation we find that such future experiments could provide strong evidence for either a normal or an inverted neutrino hierachy .
Finally we show that if a particular neutrino hierachy is assumed then this could bias cosmological parameter constraints , for example the dark energy equation of state parameter , by \mathrel { \raise 1.16 pt \hbox { $ > $ } \kern - 7.0 pt \lower 3.06 pt \hbox { { $ \scriptstyle% \sim$ } } } 1 \sigma , and the sum of masses by 2.3 \sigma .