  In Gauss-Bonnet braneworld cosmology, the Friedmann equation of our
four-dimensional universe on 3-brane is modified in a high energy regime
(Gauss-Bonnet regime), while the standard expansion law is reproduced in low
energies (standard regime). We investigate the Gauss-Bonnet braneworld
cosmological effect on the thermal relic density of cold dark matter when the
freeze-out of the dark matter occurs in the Gaugss-Bonnet regime. We find that
the resultant relic density is considerably reduced when the transition
temperature, which connects the Gauss-Bonnet regime with the standard regime,
is low enough. This result is in sharp contrast with the result previously
obtained in the Randall-Sundrum braneworld cosmology, where the relic density
is enhanced.
