Finding Evidence for Massive Neutrinos using 3D Weak Lensing

TL;DR

The paper evaluates 3D weak lensing as a probe of massive neutrinos by using 3D cosmic shear in combination with Planck CMB data. It forecasts precision on neutrino parameters and assesses the evidential power via Bayesian methods, showing that next-generation photometric surveys can constrain the total neutrino mass and the number of neutrino species with substantial, often decisive, evidence against massless models. The approach hinges on modeling the 3D shear field, employing a Fisher matrix to predict errors, and computing Bayes factors to compare competing neutrino scenarios. The findings imply significant improvements over Planck alone and demonstrate a methodology for distinguishing between neutrino models, with implications for particle physics and cosmology.

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 N_nu and the sum of their masses m_nu to an accuracy of dN_nu ~ 0.08 and dm_nu ~ 0.03 eV respectively. If in fact the masses are close to zero, then the errors weaken to dN_nu ~ 0.10 and dm_nu~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_nu and m_nu. 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_nu-3| > 0.35 and m_nu > 0.25 eV. We introduce the notion of marginalised and conditional evidence when considering evidence for individual parameter values within a multi-parameter model.

Figures (2)

• Figure 1: The expected joint evidence for the number $N_{\nu}$ and mass $m_{\nu}$ of neutrinos using 3D cosmic shear and the fiducial survey design. White='decisive', lightest gray='substantial', darkest gray='strong' and black='inconclusive'. The upper panel shows the constraints from Planck alone, the lower panel shows the constraints when 3D cosmic shear from the fiducial survey is combined with Planck.
• Figure 2: The predicted evidence for the number $N_{\nu}$ and total mass $m_{\nu}$ of neutrinos individually for 3D cosmic shear using the fiducial survey combined with a Planck prior. In each plot the solid line show the conditional evidence assuming that the other parameter is fixed at its fiducial value, the dashed line shows the marginal expected evidence when the possible values of the hidden parameter are taken into account, see Eqn. (\ref{['marginalevidence']}). The dot-dashed lines show the defining evidence limits on the Jeffery's scale where $\ln B<1$ is 'inconclusive', $1<\ln B<2.5$ is 'substantial' evidence in favour of a model, $2.5<\ln B< 5$ is 'strong', and $\ln B>5$ is 'decisive'.