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-v and the sum of their masses m(v) = Sigma(m)(i)(i) to an accuracy of Delta N-v similar to 0.08 and Delta m(v) similar to 0.03 eV, respectively. If in fact the masses are close to zero, then the errors weaken to Delta N-v similar to 0.10 and Delta m(v) similar to 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-v and m(v). 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 vertical bar N-v - 3 vertical bar greater than or similar to 0.35 and m(v) greater than or similar to 0.25 eV. We introduce the notion of marginalized and conditional evidence when considering evidence for individual parameter values within a multiparameter model.