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

In this work we update the bounds on $\sum m_ν$ from latest publicly available cosmological data and likelihoods using Bayesian analysis, while explicitly considering particular neutrino mass hierarchies. In the minimal $Λ\textrm{CDM}+\sum m_ν$ 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: $\sum m_ν<0.12$ eV (degenerate), $\sum m_ν<0.15$ eV (normal), $\sum m_ν<0.17$ eV (inverted). The bounds vary across the different mass orderings due to different priors on $\sum m_ν$. Also, we find that the normal hierarchy is very mildly preferred relative to the inverted, using both minimum $χ^2$ values and Bayesian Evidence ratios. In this paper we also provide bounds on $\sum m_ν$ considering different hierarchies in various extended cosmological models: $Λ\textrm{CDM}+\sum m_ν+r$, $w\textrm{CDM}+\sum m_ν$, $w_0 w_a \textrm{CDM}+\sum m_ν$, $w_0 w_a \textrm{CDM}+\sum m_ν$ with $w(z)\geq -1$, $Λ\textrm{CDM} + \sum m_ν + Ω_k$, and $Λ\textrm{CDM} + \sum m_ν + A_{\textrm{Lens}}$. We do not find any strong evidence of normal hierarchy over inverted hierarchy in the extended models either.