How tightly is the nuclear symmetry energy constrained by a unitary Fermi gas?

We examine critically how tightly the density dependence of nuclear symmetry energy EsymeqT is constrained by the universal equation of state of the unitary Fermi gas EUGeqT considering currently known uncertainties of higher order parameters describing the density dependence of the equation of state of isospin asymmetric nuclear matter. We found that EUGeqT does provide a useful lower boundary for the EsymeqT . However, it does not tightly constrain the correlation between the magnitude Esymeq0T and slope L unless the curvature Ksym of the symmetry energy at saturation density q0 is more precisely known. The large uncertainty in the skewness parameters affects the Esymeq0T versus L correlation by the same almost as significantly as the uncertainty in Ksym.