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 $\mathrm{\Lambda }\text{CDM}+\sum m_{\nu }$ 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: $\mathrm{\Lambda }\text{CDM}+\sum m_{\nu }+r$, $w\text{CDM}+\sum m_{\nu }$, $w_0 w_a $\text{CDM}$+\sum m_{\nu}$,$w_0 w_a $\text{CDM}$+\sum m_{\nu}$with$w(z)\geq -1$,$\Lambda $\text{CDM}$ + \sum m_{\nu} + \Omega_k$,and$\Lambda $\text{CDM}$ + \sum m_{\nu} + A_{$\text{Lens}$}$. We do not find any strong evidence of normal hierarchy over inverted hierarchy in the extended models either.