Integral representation of the cosmic microwave background spectrum
  We use an integral representation for nonthermal radiation, which is bounded
from below and above, to describe the spectrum of the cosmic microwave
background (CMB). The upper bound is given by the Rayleigh-Jeans law with a
temperature $T_{RJ}$ that can be determined by the absorption signal of 21 cm
photons, where $T_{RJ}$ represents the equilibrium temperature of photons in
the RJ tail. If $T_{RJ}>T_{CMB}$, then the lower bound allows us to conclude
that photons, additional to the remnant of the Big Bang, are needed to explain
the present CMB. These constraints are additional to other cosmological or
astrophysical constraints in the study of the distortions of the CMB brought
about by new physics particles or fields.
