  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.
