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In this work we update the bounds on $\sum m_{\nu}$ from latest publiclyavailable cosmological data and likelihoods using Bayesian analysis, whileexplicitly considering particular neutrino mass hierarchies. In the minimal$\Lambda\textrm{CDM}+\sum m_{\nu}$ model with most recent CMB data from Planck2018 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 boundsvary across the different mass orderings due to different priors on $\summ_{\nu}$. Also, we find that the normal hierarchy is very mildly preferredrelative to the inverted, using both minimum $\chi^2$ values and BayesianEvidence 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 strongevidence of normal hierarchy over inverted hierarchy in the extended modelseither.

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