We describe a calculation of electromagnetic cascading in radiation and matter in the early universe initiated by the decay of massive particles or by some other process. We have used a combination of Monte Carlo and numerical techniques which enables us to use exact cross sections, where known, for all the relevant processes. In cascades initiated after the epoch of big bang nucleosynthesis $γ$-rays in the cascades will photodisintegrate $^4$He, producing $^3$He and deuterium. Using the observed $^3$He and deuterium abundances we are able to place constraints on the cascade energy deposition as a function of cosmic time. In the case of the decay of massive primordial particles, we place limits on the density of massive primordial particles as a function of their mean decay time, and on the expected intensity of decay neutrinos.

compressed and uuencoded postscript. We now include a comparison with previous work of the photon spectrum in the cascade and the limits we calculate for the density of massive particles. The method of calculation of photon spectra at low energies has been improved. Most figures are revised. Our conclusions are substantially unchanged