Abstract Recent measurements of the spectral distortuons of the cosmic microwave background radiation (CBR) indicate that the chemical potential μ of the photon gas filling the early universe is less than O(10 −2) and might be as small as 10 −3, 10 −4. We have reinvestigated the bounds derived from this low value of μ, integrating numerically the evolution in time of the typical length scale factor of the universe, the entropy per baryon and the chemical potential of photons. A heavy “Dirac” neutrino is much more constrained than a “Majoran” one, owing to a leptonic asymmetry between the neutrino and ist antiparticle which arose at the grand-unified epoch. If μ<O(10 −4), its lifetime is less than O(10 5) s even for a 1 TeV neutrino. Finally the present density of an unstable gravitino, produced at the end of the inflation era, during the reheating, must be sufficiently small not to distort the CBR overmuch with its decay products. This results in an upper limit upon the maximal reheating temperature T max which, roughly, lies between 4 × 10 8 and 3 × 10 10 GeV if μ is less than O(10 −3).