Anomalous Matter Potentials in Earth's Inner Core: A Phenomenological Probe of Dark Matter and Light Sterile Neutrinos

Abstract

Standard treatments of Earth matter effects in neutrino oscillation experiments assume that the coherent forward scattering potential experienced by propagating neutrinos is sourced entirely by the Standard Model electron density predicted by the Preliminary Reference Earth Model (PREM). We examine how an anomalous matter potential localized in Earth's inner core, motivated by gravitationally captured dark matter or resonant mixing of active neutrinos with a light (eV-scale or lighter) sterile state, would distort the vu survival and vutove appearance probabilities relative to the Standard Model PREM expectation. Using a full three-flavor matrix-exponentiation propagation code with a four-shell PREM density profile, we parametrize the new-physics contribution as a fractional enhancement ecore of the electron-sector potential confined to the inner core (r<1221 km) and compute oscillation probabilities for near-vertically upgoing atmospheric neutrinos (L=8000to12742km). Trajectories that do not cross the inner core (L<=12500km) are essentially insensitive to ecore, reproducing the Standard Model expectation to better than 0.1%. In contrast, near-antipodal trajectories crossing the inner core (L>=12505km, corresponding to nadir angles within roughly half a degree of the vertical) show significant effects. The muon-neutrino survival probability is displaced by tens of percent for ecore=0.05to0.15 and by more than 100% at particular energies for the νμ to νe appearance channel, with a pronounced neutrinoantineutrino asymmetry that mimics, but is physically distinct from, intrinsic CP violation. These results indicate that percent-level new-physics potentials confined to the inner core are within the discovery reach of high-statistics atmospheric neutrino telescopes such as IceCube Upgrade, KM3NeT/ORCA, and next-generation megaton-scale detectors.