A possible detection of the cosmic antineutrino background in the presence of flavor effects

Lusignoli and Vignati have recently pointed out that it is in principle possible to directly detect the cosmic antineutrino background (Cν¯B) by using the rather stable isotope 163Ho as a target, which can decay into 163Dy via electron capture (EC) with a very small energy release. In this Letter we calculate the rate of the relic antineutrino capture on 163Ho nuclei against the corresponding EC decay rate by taking account of different neutrino mass hierarchies and reasonable values of θ13. We show that such flavor effects are appreciable and even important in some cases, and stress that a calorimetric measurement of the Cν¯B might be feasible in the far future.