Determining the Neutrino Mass Hierarchy with Cosmology

TL;DR

The paper investigates whether cosmology can determine the neutrino mass hierarchy by constraining individual masses with a parameterization where $m_3=\alpha\sum m_\nu$ and $m_1=m_2$. Using Fisher-matrix forecasts for Planck CMB data combined with Euclid-like weak lensing tomography, the authors show that Planck+Euclid can constrain $\sum m_\nu$ to about $3.7\times10^{-2}$ eV and measure the hierarchy parameter $\alpha$ with uncertainties around $0.19$–$0.22$ under plausible fiducials, potentially distinguishing normal from inverted hierarchies. A Bayesian evidence analysis indicates future data could provide strong support for a neutrino mass splitting over a degenerate spectrum, but mis-specifying the hierarchy can bias cosmological parameters, notably the dark energy equation of state $w$ and the total neutrino mass. Overall, the work demonstrates that upcoming cosmological surveys may probe neutrino mass differences, highlighting the need to account for mass splitting in precision cosmology to avoid biased inferences.

Abstract

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 > 1σ, and the sum of masses by 2.3σ.

Figures (6)

• Figure 1: $68\%$ and $95\%$ probability contours (two-parameter) in the plane $\alpha$-$\sum m_{\nu}$ for Planck+Euclid from our Fisher matrix calculation for the $10$-parameter space described in the text.
• Figure 2: relative error on $\alpha$ as a function of the target model for the combination Planck$+$Euclid. The fiducial value for the total mass is $\sum m_{\nu}=0.055$ eV.
• Figure 3: $68\%$$2$-parameter probability contours in the plane $\sum m_{\nu}$-$\alpha$ for Planck (green, light ellipse), Euclid (blue, dark ellipse) and the combination (red, central ellipse) from our Fisher matrix calculations for the $8$-parameter space described in the text. The plots are for fiducial values $\alpha=0.86$ (left), $\alpha=0.88$ (middle) and $\alpha=0.9$ (right).
• Figure 4: derivatives of matter power spectrum with respect to $\alpha$ for two target models. The derivative for $\alpha=1/3$ is multiplied for a factor $10$. See text for more details.
• Figure 5: absolute value of $\ln B$ as a function of $|\delta\alpha|$. The lines indicates the limits of the Jeffreys scale. On the right of the cusp is $B<1$, meaning evidence favours a more general parameterization of neutrino mass hierarchy.