Stringent constraint on the scalar-neutrino coupling constant from quintessential cosmology

An extremely light ($m_{\phi} \ll 10^{-33} {\rm eV}$), slowly-varying scalar field $\phi $ (quintessence) with a potential energy density as large as 60% of the critical density has been proposed as the origin of the accelerated expansion of the Universe at present. The interaction of this smoothly distributed component with another predominately smooth component, the cosmic neutrino background, is studied. The slow-roll approximation for generic $\phi $ potentials may then be used to obtain a limit on the scalar-neutrino coupling constant, found to be many orders of magnitude more stringent than the limits set by observations of neutrinos from SN 1987A. In addition, if quintessential theory allows for a violation of the equivalence principle in the sector of neutrinos, the current solar neutrino data can probe such a violation at the 10^{-10} level.