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

In this work we update the bounds on Sigma m(nu) from latest publicly available cosmological data and likelihoods using Bayesian analysis, while explicitly considering particular neutrino mass hierarchies. In the minimal ACDM + Sigma 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: Sigma m(nu) < 0.12 eV (degenerate), Sigma m(nu )< 0.15 eV (normal), Sigma m(nu) < 0.17eV (inverted). The bounds vary across the different mass orderings due to different priors on Sigma 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 Sigma m(nu) considering different hierarchies in various extended cosmological models: ACDM + Sigma m(nu) + r, wCDM+Sigma m(nu), w(0)w(a)CDM+Sigma m(nu), w(0)w(a)CDM+Sigma m(nu) with w(z) >= -1, ACDM+Sigma m(nu)+Omega(k), and ACDM + Sigma m(nu) + A(Lens). We do not find any strong evidence of normal hierarchy over inverted hierarchy in the extended models either.