The blackness of the cosmic microwave background spectrum as a probe of
  the distance-duality relation
  A violation of the reciprocity relation, which induces a violation of the
distance duality relation, reflects itself in a change in the normalisation of
the cosmic microwave spectrum in such a way that its spectrum is grey. We show
that existing observational constraints imply that the reciprocity relation
cannot be violated by more than 0.01% between decoupling and today. We compare
this effect to other sources of violation of the distance duality relations
which induce spectral distortion of the cosmic microwave background spectrum.
