Probing the Neutrino Mass Hierarchy beyond $Λ$CDM Model

TL;DR

This work investigates how the neutrino mass hierarchy affects cosmological inferences when allowing dynamical dark energy to vary, by encoding the hierarchy in the dimensionless parameter $Δ=(m_3-m_1)/(m_3+m_1)$. Using Planck 2015 data along with BAO, JLA, and local $H_0$ measurements, the authors employ CosmoMC/CAMB with $Δ$ as a free parameter and perform importance sampling to assess the impact of alternative priors on $Δ$ and $Σmν$, complemented by Bayesian evidence analysis. They find bimodal posteriors for $Σmν$ due to NH/IH mixtures, with NH marginally favored in ΛCDM and wCDM, but not decisively in the $w_0w_a$CDM model; priors mainly shift upper limits upward without overturning hierarchy tendencies. The results reveal degeneracies between neutrino masses and dark-energy parameters, e.g., $Σmν$ anti-correlated with $|Δ|$ and with EOS evolution, highlighting that current data cannot definitively distinguish NH from IH. Overall, a flat linear prior on $Δ$ and the $w_0w_a$CDM model are most favored by Bayesian evidence, yet the neutrino mass hierarchy remains undetermined in this cosmological context.

Abstract

Taking the neutrino oscillation data into consideration, a dimensionless parameter $Δ= (m_3-m_1)/(m_3+m_1)$ is adopted to parameterize the three neutrino mass eigenstates and the normal (positive $Δ$) or inverted (negative $Δ$) mass hierarchies in three typical cosmological models. Using the currently available cosmic observational data, several Markov Chain Monte Carlo chains are obtained with uniform priors on the free parameters at first. Applying importance sampling the results are compared with three new priors, i.e., logarithmic prior on $|Δ|$, linear and logarithmic priors on $Σm_ν$. It turns out that the three new priors increase the upper limits of neutrino mass, but do not change the tendency towards different model's preference for different hierarchies, i.e., the normal hierarchy tends to be favored by $Λ$CDM and $w$CDM, which, however, disappears in the $w_0 w_a$CDM model. In addition, the almost symmetrical contours in the $w-Δ$, $w_0-Δ$, $w_a-Δ$ planes indicate that the normal and inverted hierarchy have strong degeneracy. Finally, we perform a Bayesian model comparison analysis, finding that flat linear prior on $Δ$ and $w_0 w_a$CDM are the most preferred prior and model, respectively.

Figures (6)

• Figure 1: The masses of the three species of neutrinos and their total mass $\sum m_\nu$ with respect to the hierarchy parameter.
• Figure 2: The 1D marginalized distribution and 2D contours for the interested parameters of different dark energy models.
• Figure 3: The $68\%$ and $95\%$ C.L. contours in the $w-\Delta$ plane of $w$CDM model. The $\Lambda$CDM case with $w=-1$ is shown in the planes by the dashed lines.
• Figure 4: The $68\%$ and $95\%$ C.L. contours in the $w_0-\Delta$, $w_a-\Delta$ planes for the $w_0 w_a$CDM model. The vertical black dashed lines is $w_0=-1$ and $w_a=0$.
• Figure 5: Different priors on $\Delta$.