  We consider the decoupling of neutrinos in the early Universe in presence of
non-standard neutral current neutrino-electron interactions (NSI). We first
discuss a semi-analytical approach to solve the relevant kinetic equations and
then present the results of fully numerical and momentum-dependent
calculations, including flavor neutrino oscillations. We present our results in
terms of both the effective number of neutrino species (N_eff) and the impact
on the abundance of He-4 produced during Big Bang Nucleosynthesis. We find
that, for NSI parameters within the ranges allowed by present laboratory data,
non-standard neutrino-electron interactions do not essentially modify the
density of relic neutrinos nor the bounds on neutrino properties from
cosmological observables, such as their mass. Nonetheless, the presence of
neutrino-electron NSI may enhance the entropy transfer from electron-positron
pairs into neutrinos instead of photons, up to a value of N_eff=3.12. This is
almost three times the correction to N_eff=3 that appears for standard weak
interactions.
