  Nonstandard interaction is expected to be a crucial hint to explain the
experimental data of neutrino scattering off electrons. In this context, the
nonstandard interaction vector and axial-vector couplings are needed to be
extracted from recent experiments and a few of them are now available in the
literature. With these coupling bounds, in this paper, I explore their impacts
on the neutrinos interacting with the free electron gas in dense matter. To
this end, I compute and predict the neutrino differential cross section and
mean free path in dense matter for all those experimental bounds. Interesting
behavior in the neutrino cross sections and mean free path is found for the
different nonstandard interaction couplings from different experiment
constraints. I also found that the neutrino cross-section and mean free path in
the dense matter are very sensitive to values and signs of the nonstandard
interaction couplings, leading to different prediction results to the Standard
Model cross-section and mean free path.
