Relic neutrino decay solution to the excess radio background

The excess radio background detected by ARCADE 2 represents a puzzle within the standard cosmological model. There is no clear viable astrophysical solution, and therefore, it might indicate the presence of new physics. Radiative decays of a relic neutrino ν_i (either i = 1, or i = 2, or i = 3) into a sterile neutrino ν _s, assumed to be quasi-degenerate, provide a solution that currently evades all constraints posed by different cosmological observations and reproduces very well the ARCADE 2 data. We find a very good fit to the ARCADE 2 data with best fit values τ_i = 1.46 × 10²¹ s and Δm_i = 4.0 × 10^-5 eV, where τ_i is the lifetime and Δm_i is the mass difference between the decaying active neutrino and the sterile neutrino. On the other hand, if relic neutrino decays do not explain ARCADE 2 data, then these place a stringent constraint Δm_i^3/2 τ_i ≳ 2 × 10¹⁴ eV^3/2 s in the range 1.4 × 10^-5 eV < Δm_i < 2.5 × 10^-4 eV. The solution also predicts a stronger 21 cm absorption global signal than the predicted one from the ΛCDM model, with a contrast brightness temperature T ₂₁ = -238⁺²¹_-20 mK (99% C.L.) at redshift z ≃ 17. This is in mild tension with the even stronger signal found by the EDGES collaboration, T ₂₁ = - 500⁺²⁰⁰_-200 mK, suggesting that this might have been overestimated, possibly receiving a contribution from some unidentified foreground source.