Cosmic microwave background anisotropy in the decaying neutrino cosmology

It is attractive to suppose for several astrophysical reasons that the universe has close to the critical density in light (~30 eV) neutrinos which decay radiatively with a lifetime of ~10^{23} sec. In such a cosmology the universe is reionized early and the last scattering surface of the cosmic microwave background significantly broadened. We calculate the resulting angular power spectrum of temperature fluctuations in the cosmic microwave background. As expected the acoustic peaks are significantly damped relative to the standard case. This would allow a definitive test of the decaying neutrino cosmology with the forthcoming MAP and PLANCK surveyor missions.