  Considering the non-Newtonian gravity proposed in the grand unification
theories, we show that the stability and observed global properties of neutron
stars can not rule out the super-soft nuclear symmetry energies at
supra-saturation densities. The degree of possible violation of the
Inverse-Square-Law of gravity in neutron stars is estimated using an Equation
of State (EOS) of neutron-rich nuclear matter consistent with the available
terrestrial laboratory data.
