Capability of Cosmic Gravitational Focusing on Identifying the Neutrino Mass Ordering

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 (NMO). Upon incorporating the projected CGF sensitivity at DESI, the preference for the normal ordering (NO) with a prior $\sum m_\nu > 0.509\,{\rm eV}$ would increase from the original 89.9\% of the current clustering method with both DESI BAO and CMB to 98.2\% while the inverted ordering (IO) 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.