Finding evidence for massive neutrinos using 3D weak lensing

In this paper we investigate the potential of 3D cosmic shear to constrain massive neutrino parameters. We find that if the total mass is substantial (near the upper limits from large scale structure, but setting aside the Ly alpha limit for now), then 3D cosmic shear+Planck is very sensitive to neutrino mass and one may expect that a next generation photometric redshift survey could constrain the number of neutrinos N_ν and the sum of their masses m_ν=∑ᵢmᵢ to an accuracy of ΔN_ν~0.08 and Δm_ν~0.03 eV, respectively. If in fact the masses are close to zero, then the errors weaken to ΔN_ν~0.10 and Δm_ν~0.07 eV. In either case there is a factor 4 improvement over Planck alone. We use a Bayesian evidence method to predict joint expected evidence for N_ν and m_ν. We find that 3D cosmic shear combined with a Planck prior could provide ``substantial'' evidence for massive neutrinos and be able to distinguish ``decisively'' between many competing massive neutrino models. This technique should ``decisively'' distinguish between models in which there are no massive neutrinos and models in which there are massive neutrinos with |N_ν-3|0.35 and m_ν0.25 eV. We introduce the notion of marginalized and conditional evidence when considering evidence for individual parameter values within a multiparameter model.