Determining the Neutrino Mass Hierarchy with Cosmology

Francesco de Bernardis
Physics Department and Sezione INFN, University of Rome “La Sapienza”


Cosmological data are known to be a powerful tool to constrain neutrino mass scale. Sensitivity of Cosmology to neutrino mass arise essentially from the peculiar imprint left by total neutrino mass on growth of structure in the Universe. In recent years atmospheric and solar neutrinos experiments have suggested the existence of differences between neutrino masses through observations of flavour oscillations. The effect on Cosmology of a splitting in neutrino masses is generally smaller than that due to the total mass and can be neglected in analysing current cosmological data. Nevertheless in the near future various experiments will reach a much higher accuracy in reconstructing matter power spectrum and could in principle become sensitive also to single 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.