In this paper, we have discussed a (1 + 9)-dimensional open cosmological model motivated from N = 2 maximal supergravity arguments characterized by the presence of a wormhole connected to the extra dimensions part and a Gauss–Bonnet (GB) curvature corrections. The universe is dominated by dark energy and cold dark matter (CDM) which emerged from extra dimensions as supported by recent phenomenological and observational arguments. By assuming that the wormhole in the outer/inner regions of the halos of galaxies is characterized by a CDM profile density, it was revealed that the universe is expanding acceleratedly with time, dominated by a microscopic traversable wormhole and dark energy. The role of the dominance of the GB term is discussed and the model is confronted with astrophysical observations.