Can the Copernican principle be tested using the cosmic neutrino background

The Copernican principle, stating that we do not occupy any special place in our universe, is usually taken for granted in modern cosmology. However recent observational supernova data indicate that we may live in the under-dense center of our universe, which challenges the Copernican principle. It thus becomes urgent and important to test the Copernican principle via cosmological observations. Taking into account that unlike cosmic photons, cosmic neutrinos of different energies come from different places to us, along different worldlines, we here propose using the cosmic neutrino background as a test of the Copernican principle. It is shown that from the theoretical perspective, the cosmic neutrino background can allow one to determine whether the Copernican principle is valid or not, but to implement such an observation, larger neutrino detectors are called for.