Cosmological constraints on neutrino mass within consistent cosmological models* * We acknowledge the use of HPC Cluster of ITP-CAS. XZ is supported by the National Natural Science Foundation of China (12005183). QGH is supported by the National Natural Science Foundation of China (12250010, 11975019, 11991052, 12047503), and the Key Research Program of Frontier Sciences, CAS, (ZDBS-LY-7009)

Recently, the emergence of cosmological tension has raised doubts about the consistency of the ΛCDM model. To constrain the neutrino mass within a consistent cosmological framework, we investigate three massive neutrinos with normal hierarchy (NH) and inverted hierarchy (IH) in both the axion-like early dark energy (Axi-EDE) and AdS-EDE models. We use joint datasets including the cosmic microwave background power spectrum from Planck 2018, Pantheon of type Ia supernova, baryon acoustic oscillation, and data from SH0ES. For the νAxi-EDE model, we obtain < 0.152 eV and < 0.178 eV, whereas for the νAdS-EDE model, we find < 0.135 eV and < 0.167 eV. Our results exhibit a preference for NH in both the νAxi-EDE and νAdS-EDE models.