If there are scalar particles of small or moderate mass coupled very weakly to Dirac neutrinos, in a minimal way, then neutrino-anti-neutrino clouds of sufficient number density can experience an instability in which helicities are suddenly reversed. The predicted collective evolution is many orders of magnitude faster than given by cross-section calculations. The instabilities are the analogue of the ``flavor-angle" instabilities (enabled by the Z exchange force) that may drive very rapid flavor exchange among the neutrinos that emerge from a supernova. These exchanges do require a tiny seed in addition to the scalar couplings, but the transition time is proportional to the negative of the logarithm of the seed strength, so that the size of this parameter is comparatively unimportant. For our actual estimates we use a tiny non-conservation of leptons; an alternative would be a neutrino magnetic moment in a small magnetic field. The possibility of a quantum fluctuation as a seed is also discussed. Operating in the mode of putting limits on the coupling constant of the scalar field, for the most minimal coupling scheme, with independent couplings to all three $ν$, we find a rough limit on the dimensionless coupling constant for a neutrino-flavor independent coupling of $G<10^{-10}$, to avoid the effective number of light neutrinos in the early universe being essentially six. If, on the other hand, we wish to fine-tune the model to give a more modest excess (over three) in the effective neutrino number, as may be needed according to recent WMAP analyses, it is easy to do so.
\pacs{13.15.+g}
Istituto Nazionale di Fisica Nucleare (INFN)（意大利国家核物理研究所）；Gran Sasso Science Institute (GSSI)（格兰萨索科学研究所）；Max-Planck-Institut für Physik（马克斯·普朗克物理学研究所）；Universität Hamburg（汉堡大学）
Single-wave solutions of the neutrino fast flavor system. Part II. Weak instabilities and their resonant behavior
Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器）；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）；Gran Sasso Science Institute (GSSI)（格兰萨索科学研究所）；Max-Planck-Institut für Physik（马克斯·普朗克物理研究所）
Institute for Particle Physics Phenomenology, Durham University（达勒姆大学粒子物理现象学研究所）；Center for Particle Cosmology, Department of Physics and Astronomy, University of Pennsylvania（宾夕法尼亚大学物理与天文学系粒子宇宙学中心）
