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

We examine critically how tightly the density dependence of nuclear symmetry energy esym is constrained by the universal equation of state (EOS) of the unitary Fermi gas $E_{rm{UG}}(rho)$ 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 $E_{rm{UG}}(rho)$ does provide a useful lower boundary for the esym. However, it does not tightly constrain the correlation between the magnitude $E_{rm{sym}}(rho_0)$ and slope $L$ unless the curvature $K_{rm{sym}}$ of the symmetry energy at saturation density $rho_0$ is more precisely known. The large uncertainty in the skewness parameters affects the $E_{rm{sym}}(rho_0)$ versus $L$ correlation by the same almost as significantly as the uncertainty in $K_{rm{sym}}$.