In this paper we investigate how well Planck and Lyman-α forest data will be able to constrain the sum of the neutrino masses, and thus, in conjunction with flavor oscillation experiments, be able to determine the absolute masses of the neutrinos. It seems possible that Planck, together with a Lyman-α survey, will be able to put pressure on an inverted hierarchial model for the neutrino masses. However, even for optimistic assumptions of the precision of future Lyman-α data sets, it will not be possible to confirm a minimal-mass normal hierarchy.
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Gratton et al. (2008) studied this question.
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