# Quantifying the tension between cosmological and terrestrial constraints on neutrino masses

## TL;DR

This paper assesses the potential tension between cosmological and terrestrial constraints on neutrino masses, emphasizing the importance of neutrino mass ordering and the precision needed in future measurements to distinguish scenarios.

## Contribution

It introduces statistical methods to quantify tensions between cosmological and terrestrial neutrino mass limits, highlighting the impact of neutrino mass ordering assumptions.

## Key findings

- Tension depends on whether normal or inverted ordering is assumed.
- Rejecting inverted ordering requires future cosmological measurements with <0.02 eV accuracy.
- Current and forecasted data show potential for distinguishing mass orderings with improved precision.

## Abstract

The sensitivity of cosmology to the total neutrino mass scale $\Sigma m_\nu$ is approaching the minimal values required by oscillation data. We study quantitatively possible tensions between current and forecasted cosmological and terrestrial neutrino mass limits by applying suitable statistical tests such as Bayesian suspiciousness, parameter goodness-of-fit tests, or a parameter difference test. In particular, the tension will depend on whether the normal or the inverted neutrino mass ordering is assumed. We argue, that it makes sense to reject inverted ordering from the cosmology/oscillation comparison only if data are consistent with normal ordering. Our results indicate that, in order to reject inverted ordering with this argument, an accuracy on the sum of neutrino masses $\sigma ({m_\nu})$ of better than 0.02~eV would be required from future cosmological observations.