Room for New Physics in the Rayleigh-Jeans Tail of the Cosmic Microwave Background

We show that, despite stringent constraints on the shape of the main part of the cosmic microwave background (CMB) spectrum, there is considerable room for its modification within its Rayleigh-Jeans (RJ) end, ω≪T_{CMB}. We construct explicit new physics models that give an order one (or larger) increase of photon count in the RJ tail, which can be tested by existing and upcoming experiments aiming to detect the cosmological 21 cm emission or absorption signal. This class of models stipulates the decay of unstable particles to dark photons A^{'} that have a small mass, m_{A^{'}}∼10^{-14}-10^{-9}  eV, nonvanishing mixing angle ε with electromagnetism, and energies much smaller than T_{CMB}. The nonthermal number density of dark photons can be many orders of magnitude above the number density of CMB photons, and even a small probability of A^{'}→A oscillations, for values as small as ε∼10^{-9}, can significantly increase the number of RJ photons. In particular, we show that resonant oscillations of dark photons into regular photons in the interval of redshifts 20