Can we measure the neutrino mass hierarchy in the sky?

TL;DR

This paper investigates whether future cosmological observations can determine the neutrino mass hierarchy by analyzing the matter power spectrum, highlighting potential challenges and implications for neutrino physics.

Contribution

It explores the potential of cosmological probes to distinguish neutrino hierarchies and discusses subtleties that could lead to false detections.

Findings

Cosmological experiments could differentiate neutrino hierarchies with substantial evidence.

Precise measurements of the matter power spectrum are crucial for hierarchy determination.

Potential spurious claims may arise due to subtleties in data interpretation.

Abstract

Cosmological probes are steadily reducing the total neutrino mass window, resulting in constraints on the neutrino-mass degeneracy as the most significant outcome. In this work we explore the discovery potential of cosmological probes to constrain the neutrino hierarchy, and point out some subtleties that could yield spurious claims of detection. This has an important implication for next generation of double beta decay experiments, that will be able to achieve a positive signal in the case of degenerate or inverted hierarchy of Majorana neutrinos. We find that cosmological experiments that nearly cover the whole sky could in principle distinguish the neutrino hierarchy by yielding 'substantial' evidence for one scenario over the another, via precise measurements of the shape of the matter power spectrum from large scale structure and weak gravitational lensing.