  We calculate the symmetry energy in cold dense matter both in the normal
quark phase and in the 2-color superconductor (2SC) phase. For the normal
phase, the thermodynamic potential is calculated by using hard dense loop (HDL)
resummation to leading order, where the dominant contribution comes from the
longitudinal gluon rest mass. The effect of gluonic interaction to the symmetry
energy, obtained from the thermodynamic potential, was found to be small. In
the 2SC phase, the non-perturbative BCS paring gives enhanced symmetry energy
as the gapped states are forced to be in the common Fermi sea reducing the
number of available quarks that can contribute to the asymmetry. We used high
density effective field theory to estimate the contribution of gluon
interaction to the symmetry energy. Among the gluon rest masses in 2SC phase,
only the Meissner mass has iso-spin dependence although the magnitude is much
smaller than the Debye mass. As the iso-spin dependence of gluon rest masses is
even smaller than the case in the normal phase, we expect that the contribution
of gluonic interaction to the symmetry energy in the 2SC phase will be minimal.
The different value of symmetry energy in each phase will lead to different
prediction for the particle yields in heavy ion collision experiment.
