Current upper bounds on the sum of 3 active neutrino masses , \sum m _ { \nu } from analyses of cosmological data in the backdrop of \Lambda \textrm { CDM } + \sum m _ { \nu } model are close to the minimum sum of neutrino masses required by the inverted hierarchy , which is around 0.1 eV .
However , these analyses are usually done with the assumption of degenerate masses , which is not a good approximation any more since the bounds are strong enough that the neutrino mass-squared splittings can no longer be considered negligible .
In this work we update the bounds on \sum m _ { \nu } from latest publicly available cosmological data and likelihoods 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 } < 0.121 eV ( degenerate ) , \sum m _ { \nu } < 0.146 eV ( normal ) , \sum m _ { \nu } < 0.172 eV ( inverted ) ; i.e. , the bounds vary significantly across the different mass orderings .
Also , we find that the normal hierarchy is very mildly preferred relative to the inverted : \Delta \chi ^ { 2 } \equiv \chi ^ { 2 } _ { \textrm { NH } } - \chi ^ { 2 } _ { \textrm { IH } } = -0.95 ( best-fit ) .
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 from looking at the \chi ^ { 2 } values in the extended models either .
However the mass bounds do differ across different hierarchies in the extended models also .
In particular , using the ( unphysical ) degenerate approximation leads to more aggressive constraints than in the normal or inverted hierarchies , and gives a wrong notion about how strong the bounds really are .