Identifying Neutrino Mass Ordering with Cosmic Gravitational Focusing

The cosmic gravitational focusing (CGF) of relic neutrinos can provide an independent measurement of the absolute neutrino masses $m_i$ with fourth-power dependence ($m^4_i$). We demonstrate in this paper for the first time how this can help identifying the neutrino mass ordering, using the fact that total mass falling below the inverted ordering threshold allows the discrimination of the inverted ordering. Upon incorporating the projected CGF sensitivity at DESI, the preference for the normal ordering with a prior $\sum m_i > 0.059\,{\rm eV}$ would increase from the original 89.9\% of the existing matter clustering method with the DESI analysis to 98.2\% while the inverted ordering is further disfavored from 10.1\% to 1.8\%. We also show how this can affect the prospects of the neutrinoless double beta decay and single beta decay measurements.