# Updated results on neutrino mass and mass hierarchy from cosmology with Planck 2018 likelihoods

## TL;DR

This paper updates cosmological bounds on the sum of neutrino masses using Planck 2018 data, considering different mass hierarchies and extended models, finding mild preference for normal hierarchy but no strong evidence.

## Contribution

It provides the latest Bayesian constraints on neutrino mass sum across various hierarchies and extended cosmological models using comprehensive Planck and BAO data.

## Key findings

- 95% CL bounds: <0.12 eV (degenerate), <0.15 eV (normal), <0.17 eV (inverted)
- Normal hierarchy is mildly preferred over inverted
- No strong evidence favoring one hierarchy in extended models

## Abstract

In this work we update the bounds on $\sum m_{\nu}$ from latest publicly available cosmological data and likelihoods using Bayesian analysis, while explicitly considering particular neutrino mass hierarchies. In the minimal $\Lambda\textrm{CDM}+\sum m_{\nu}$ model with most recent CMB data from Planck 2018 TT,TE,EE, lowE, and lensing; and BAO data from BOSS DR12, MGS, and 6dFGS, we find that at 95\% C.L. the bounds are: $\sum m_{\nu}<0.12$ eV (degenerate), $\sum m_{\nu}<0.15$ eV (normal), $\sum m_{\nu}<0.17$ eV (inverted). The bounds vary across the different mass orderings due to different priors on $\sum m_{\nu}$. Also, we find that the normal hierarchy is very mildly preferred relative to the inverted, using both minimum $\chi^2$ values and Bayesian Evidence ratios. In this paper we also provide bounds on $\sum m_{\nu}$ considering different hierarchies in various extended cosmological models: $\Lambda\textrm{CDM}+\sum m_{\nu}+r$, $w\textrm{CDM}+\sum m_{\nu}$, $w_0 w_a \textrm{CDM}+\sum m_{\nu}$, $w_0 w_a \textrm{CDM}+\sum m_{\nu}$ with $w(z)\geq -1$, $\Lambda \textrm{CDM} + \sum m_{\nu} + \Omega_k$, and $\Lambda \textrm{CDM} + \sum m_{\nu} + A_{\textrm{Lens}}$. We do not find any strong evidence of normal hierarchy over inverted hierarchy in the extended models either.