Cosmology and the neutrino mass ordering

TL;DR

This paper tackles whether cosmological measurements can exclude the inverted neutrino mass ordering (IO). It introduces a Bayesian framework to compute the posterior odds for NO versus IO by marginalizing over cosmological parameters and the lightest neutrino mass, using data such as Planck CMB and large-scale structure. Applying the method to current Planck+BAO+$H_0$ within a $\Lambda$CDM+$\Sigma$ model yields $\Sigma < 0.14$ eV (95% CL) and modest IO discrimination ($p_I \sim 0.35$–$0.392$, depending on priors). Forecasts for EUCLID-like data suggest $\Sigma = 0.060 \pm 0.021$ eV and $p_I \approx 0.08$ (NO:IO ≈ 12:1), indicating that future cosmology could robustly favor NO. The work provides a principled, combineable framework to integrate cosmology with oscillation results and to report statistically meaningful evidence about the neutrino mass ordering.

Abstract

We propose a simple method to quantify a possible exclusion of the inverted neutrino mass ordering from cosmological bounds on the sum of the neutrino masses. The method is based on Bayesian inference and allows for a calculation of the posterior odds of normal versus inverted ordering. We apply the method for a specific set of current data from Planck CMB data and large-scale structure surveys, providing an upper bound on the sum of neutrino masses of 0.14 eV at 95% CL. With this analysis we obtain posterior odds for normal versus inverted ordering of about 2:1. If cosmological data is combined with data from oscillation experiments the odds reduce to about 3:2. For an exclusion of the inverted ordering from cosmology at more than 95% CL, an accuracy of better than 0.02 eV is needed for the sum. We demonstrate that such a value could be reached with planned observations of large scale structure by analysing artificial mock data for a EUCLID-like survey.

Figures (3)

• Figure 1: Posterior likelihood function from current data (Planck+BAO+$H_0$). The left panel shows the posterior likelihood function for $\Sigma$, where we indicate the predicted values for NO and IO in the case of $m_0 = 0$; the width of the lines corresponds to $\pm 2\sigma$ uncertainty due to current oscillation data. The gray shaded region indicates the one-sided upper bound on $\Sigma$ at 95% CL (flat prior in $\Sigma$). The right panel shows the posterior likelihood as a function of $m_0$ for NO and IO with appropriate relative normalization. The dashed, dot-dashed, solid curves correspond to the approximation that 1, 2, 3 massive neutrinos contribute to $\Sigma$ (see text for details).
• Figure 2: Posterior likelihood function from simulated future data (EUCLID+Planck CMB). The left panel shows the posterior likelihood function for $\Sigma$ for a fiducial model with one massive neutrino with $m_\nu = 0.06$ eV and two massless neutrinos. We indicate the predicted values for NO and IO in the case of $m_0 = 0$; the width of the lines corresponds to $\pm 2\sigma$ uncertainty due to current oscillation data. The gray shaded region indicates the one-sided upper bound on $\Sigma$ at 95% CL (flat prior in $\Sigma$). The right panel shows the posterior likelihood as a function of $m_0$ for NO and IO with appropriate relative normalization.
• Figure 3: Illustration of the potential to exclude IO for a Gaussian toy likelihood. Solid curves show the probability of inverted ordering being correct as a function of the observed value of $\Sigma$ for different assumptions about the obtained accuracy from cosmology, $\sigma_{\rm obs}$, according to the legend (values in eV). We assume equal prior probabilities for NO and IO. The dashed curves show the probability of observing a value of $\Sigma$ equal or less than the one shown on the horizontal axis assuming that the true ordering is normal and $m_0 = 0$ for the assumed accuracy on $\Sigma$. The thin vertical line indicates the median value for $\Sigma$ for NO and $m_0=0$. The star and the triangle show approximately the cases of current and prospective data, respectively, as analysed in sec. \ref{['sec:data']}.