Best-case scenarios for neutrino capture experiments

A direct discovery of the cosmic neutrino background would bring to a closure the searches for relic left-over radiation predicted by the Hot Big Bang cosmology. Recently, the KATRIN experiment put a limit on the local relic neutrino overdensity with respect to the cosmological predicted average value at η ≲ 10¹¹ [Phys. Rev. Lett. 129 (2022) 011806]. In this work, we first examine to what extent such values of η are conceivable. We show that even under cavalier assumptions, a cosmic origin of η ≳ 10⁴ seems out of reach (with the caveat of forming bound objects under a new force,) but find that a hypothetical local source of low-energy neutrinos could achieve η ∼ 10¹¹. Second, when such values are considered, we point out that the experimental signature in KATRIN and other neutrino-capture experiments changes, contrary to what has hitherto been assumed. Our results are model-independent and maximally accommodating as they only assume the Pauli exclusion principle. As intermittent physics target in the quest for CνB detection, we identify an experimental sensitivity to η ∼ 10⁴ for which conceivable sources exist; to resolve the effect of a degenerate Fermi gas for such overdensity an energy resolution of 10 meV is required.