  Coherent forward scattering processes by neutrino-scalar nonstandard
interactions (SNSI) induce an effective neutrino mass. In the Early Universe, a
large neutrino effective mass restricts the production of neutrinos. The SNSI
effect is modulated by two effective couplings, these account for the coupling
between neutrinos and electrons/positrons, $G_{\rm eff}$, and the neutrino
self-interaction, $G_{\rm S}$. These parameters are directly related to the
effective number of relativistic species and non-zero values imply a smaller
than expected $N_{\rm eff}$. We employ big bang nucleosynthesis to constraint
the SNSI effect. We find that $ G_{\rm eff }< 1.2$ MeV$^{-2}$ and $ G_{\rm S }<
2.0 \times 10^{7}$ MeV$^{-2}$ at 68\% CL. For a scalar mass in the range
$10^{-15} {\rm eV}\lesssim m_{\phi}\lesssim 10^{-5}{\rm eV}$, our
neutrino-scalar coupling constraint is more restrictive than any previous
result.
