Probing dark matter inside Earth using atmospheric neutrino oscillations at INO-ICAL

The interior of Earth's core can be explored using weak interactions of atmospheric neutrinos. This would complement gravitational and seismic measurements, paving the way for multimessenger tomography of Earth. Oscillations of atmospheric neutrinos passing through Earth are affected by the ambient electron density. We demonstrate that atmospheric neutrinos can probe the possible existence of dark matter inside Earth's core in a unique way - by measuring the amount of baryonic matter using neutrino oscillations. We find that a detector like ICAL at INO with muon charge identification capability can be sensitive to dark matter with $\sim5\%-6\%$ mass of Earth, at 1$\sigma$ level with 500 kt$\cdot$yr exposure. We show that while it will not be possible to identify the dark matter profile using neutrino oscillation experiments, the baryonic matter profile inside the core can be probed with atmospheric neutrinos.