Can we measure the neutrino mass hierarchy in the sky?

TL;DR

The paper investigates whether cosmological sky data can determine the neutrino mass hierarchy. It introduces a hierarchy parameter Δ to encode the ordering and analyzes its imprint on the matter power spectrum P(k). Using Fisher-matrix forecasts for cosmic-variance-limited large-scale structure and weak lensing, plus Planck-like CMB data, it finds a bimodal likelihood in Δ which complicates hierarchy inference, but under optimistic full-sky surveys the normal vs inverted hierarchies could be distinguished for Σ below about 0.15–0.2 eV with substantial Bayesian evidence. It also discusses complementarity with neutrinoless double beta decay experiments and suggests Euclid- or SKA-like surveys could approach the required sensitivity, though practical feasibility remains challenging.

Abstract

Cosmological probes are steadily reducing the total neutrino mass window, resulting in constraints on the neutrino-mass degeneracy as the most significant outcome. In this work we explore the discovery potential of cosmological probes to constrain the neutrino hierarchy, and point out some subtleties that could yield spurious claims of detection. This has an important implication for next generation of double beta decay experiments, that will be able to achieve a positive signal in the case of degenerate or inverted hierarchy of Majorana neutrinos. We find that cosmological experiments that nearly cover the whole sky could in principle distinguish the neutrino hierarchy by yielding 'substantial' evidence for one scenario over the another, via precise measurements of the shape of the matter power spectrum from large scale structure and weak gravitational lensing.

Figures (5)

• Figure 1: Left: constraints from neutrino oscillations and from cosmology in the $m$-$\Sigma$ plane. Right: constraints from neutrino oscillations (shaded regions) and from cosmology in the $\Sigma$-$\Delta$ plane. In this parameterization the sign of $\Delta$ specifies the hierarchy.
• Figure 2: Dependence of $P(k)$ on the parameter $\Delta$ at $z=0$, for fixed $\Sigma$ and several values of $\Delta$. The dependence is expressed as fractional variation in $P(k)$ for a unit variation in $\Delta$. For this value of the total mass $\Sigma$, normal (inverted) hierarchy correspond to $\Delta \sim 0.05$ ($\Delta=-0.05$).
• Figure 3: $\Delta \chi^2$ as a function of the degeneracy parameter $\Delta$ for a fixed total neutrino mass $\Sigma$ (and fixed cosmology). This is a section along a $\Sigma$=constant line of Fig. \ref{['fig:0']} of the quantity $-2\ln L$ as it would be seen by a Fisher matrix approach for a IH fiducial model. The vertical lines show the location of the normal and inverted hierarchy. Note the bimodal distribution of the $\ln L$ surface, which makes the determination of the hierarchy from measurements of the shape of the power spectrum extremely challenging. The $\Delta \chi^2$ normalization matches that achievable from an ideal weak lensing survey as described in the text.
• Figure 4: LSS (left) and Weak Lensing (right) forecasts for neutrino mass parameters $\Sigma$ and $\Delta$. We assume the LSS survey consists of a comoving volume of $600$ Gpc$^3$ at $z=2$ and $2000$ Gpc$^3$ at $z=5$. The Weak Lensing survey covers $40$,$000$ sq. deg. with a median redshift of $3.0$ and a number density of $150$ galaxies per square arcminute. Several fiducial models ($\Sigma$,$\Delta$) were used to derive by Fisher matrix approach the expected errors. The upper panel show the $1$-$\sigma$ errors on $\Delta$ and $\Sigma$, the errors in $\Sigma$ are so small that are barely visible. The lower panel shows the expected evidence ratio between the normal and inverted constraints as a function of neutrino mass. The dashed line shows the $\ln B=1$ level: in Jeffrey's scale $\ln B<1$ is 'inconclusive' evidence, and $1<\ln B<2.5$ corresponds to 'substantial' evidence.
• Figure 5: Role of cosmology in determining the nature of neutrino mass. Future neutrinoless double beta decay ($0\nu \beta beta$) experiments and future cosmological surveys will be highly complementary in addressing the question of whether neutrinos are Dirac or Majorana particles. Next generation means near future experiments whose goal is to reach a sensitivity to the neutrinoless double beta decay effective mass of $0.01$ eV. We can still find two small windows where this combination of experiments will not be able to give a definite answer, but this region is much reduced by combining $0\nu \beta beta$ and cosmological observations.