  We show that despite stringent constraints on the shape of the main part of
the CMB spectrum, there is considerable room for its modification within its
Rayleigh-Jeans (RJ) end, $\omega \ll T_{\rm CMB}$. 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/absorption signal. This class of models
stipulates the decay of unstable particles to dark photons, $A'$, that have a
small mass, $m_{A'} \sim 10^{-14} - 10^{-9}$ eV, non-vanishing mixing angle
$\epsilon$ with electromagnetism, and energies much smaller than $T_{\rm CMB}$.
The non-thermal number density of dark photons can be many orders of magnitude
above the number density of CMB photons, and even a small probability of $A'\to
A$ oscillations, for values of as small as $\epsilon \sim 10^{-9}$, 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 $20 < z < 1700$ can be invoked as an explanation of the recent
tentative observation of a stronger-than-expected absorption signal of 21 cm
photons. We present a model that realizes this possibility, where milli-eV mass
dark matter decays to dark photons, with a lifetime longer than the age of the
Universe.
