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

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.