Finding Evidence for Massive Neutrinos using 3D Weak Lensing
Abstract
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 LSS, 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 Nnu and the sum of their masses mnu to an accuracy of dNnu ~ 0.08 and dmnu ~ 0.03 eV respectively. If in fact the masses are close to zero, then the errors weaken to dNnu ~ 0.10 and dmnu~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 Nnu and mnu. 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 |Nnu-3| > 0.35 and mnu > 0.25 eV. We introduce the notion of marginalised and conditional evidence when considering evidence for individual parameter values within a multi-parameter model.