Improved treatment of cosmic microwave background fluctuations induced by a late-decaying massive neutrino

A massive neutrino which decays after recombination $(t>~{10}^{13}\hspace{0.5em}\sec )$ into relativistic decay products produces an enhanced integrated Sachs-Wolfe effect, allowing constraints to be placed on such neutrinos from present cosmic microwave background anisotropy data. Previous treatments of this problem have approximated the decay products as an additional component of the neutrino background. This approach violates energy-momentum conservation, and we show that it leads to serious errors for some neutrino masses and lifetimes. We redo this calculation more accurately, by correctly incorporating the spatial distribution of the decay products. For low neutrino masses and long lifetimes, we obtain a much smaller distortion in the CMB fluctuation spectrum than have previous treatments. We combine these new results with a recent set of CMB data to exclude the mass and lifetime range $m_h>100\mathrm{}\hspace{0.5em}\mathrm{eV},$ $\tau >{10}^{12}$ sec. Masses as low as 30 eV are excluded for a narrower range in lifetime.