Determining the Neutrino Mass Hierarchy with Cosmology
  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 > 1\sigma, and the
sum of masses by 2.3\sigma.
