Constraining invisible neutrino decays with the cosmic microwave background

Precision measurements of the acoustic peaks of the cosmic microwave background indicate that neutrinos must be freely streaming at the photon decoupling epoch when T ~ 0.3 eV. This requirement implies restrictive limits on ``secret neutrino interactions,'' notably on neutrino Yukawa couplings with hypothetical low-mass (pseudo)scalars \phi. For diagonal couplings in the neutrino mass basis we find g < 1 x 10^-7, comparable to limits from supernova 1987A. For the off-diagonal couplings and assuming hierarchical neutrino masses we find g < 1 x 10^-11 (0.05 eV/m)^2 where m is the heavier mass of a given neutrino pair connected by g. This stringent limit excludes that the flavor content of high-energy neutrinos from cosmic-ray sources is modified by \nu -> \nu' + \phi decays on their way to Earth.