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 \(E_{{\text {sym}}}(\rho )\,\)is constrained by the universal equation of state of the unitary Fermi gas \(E_{{\text {UG}}}(\rho )\) 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 \(E_{{\text {UG}}}(\rho )\) does provide a useful lower boundary for the \(E_{{\text {sym}}}(\rho )\,\). However, it does not tightly constrain the correlation between the magnitude \(E_{{\text {sym}}}(\rho _0)\) and slope L unless the curvature \(K_{{\text {sym}}}\) of the symmetry energy at saturation density \(\rho _0\) is more precisely known. The large uncertainty in the skewness parameters affects the \(E_{{\text {sym}}}(\rho _0)\) versus L correlation by the same almost as significantly as the uncertainty in \(K_{{\text {sym}}}\).