Determining the neutrino mass hierarchy with cosmology

The combination of current large-scale structure and cosmic microwave background anisotropies data can place strong constraints on the sum of the neutrino masses. Here we show that future cosmic shear experiments, in combination with cosmic microwave background 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 nondegenerate 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 hierarchy. Finally we show that if a particular neutrino hierarchy is assumed then this could bias cosmological parameter constraints, for example, the dark energy equation of state parameter, by > or approx. 1σ, and the sum of masses by 2.3σ. We finally discuss the impact of uncertainties on the theoretical modeling of nonlinearities. The results presented in this analysis are obtained under an approximation to the nonlinear power spectrum. This significant source of uncertainty needs to be addressed in future work.