What originally symbolized the "Globus cruciger"?

Holding the world in one's hand, or more ominously, under one's foot, has been used as a symbol since antiquity. To citizens of the Roman Empire, the globe held by the god Jupiter represented the world, as the dominion held by the emperor. With the growth of Christianity in the 5th century, the orb was topped with a cross (hence globus cruciger), symbolising the Christian God's dominion over the world.