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

In this work we update the bounds on $sum m_{ u}$ from latest publicly available cosmological data and likelihoods using Bayesian analysis, while explicitly considering particular neutrino mass hierarchies. In the minimal $Lambdatextrm{CDM}+sum m_{ u}$ 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: $sum m_{ u}<0.12$ eV (degenerate), $sum m_{ u}<0.15$ eV (normal), $sum m_{ u}<0.17$ eV (inverted). The bounds vary across the different mass orderings due to different priors on $sum m_{ u}$. 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 $sum m_{ u}$ considering different hierarchies in various extended cosmological models: $Lambdatextrm{CDM}+sum m_{ u}+r$, $wtextrm{CDM}+sum m_{ u}$, $w_0 w_a textrm{CDM}+sum m_{ u}$, $w_0 w_a textrm{CDM}+sum m_{ u}$ with $w(z)geq -1$, $Lambda textrm{CDM} + sum m_{ u} + Omega_k$, and $Lambda textrm{CDM} + sum m_{ u} + A_{textrm{Lens}}$. We do not find any strong evidence of normal hierarchy over inverted hierarchy in the extended models either.