User blog comment:LurkerLordB/Religion in a world without Christianity/@comment-1630894-20120425221439/@comment-1593341-20120429014747

The cult of Sol seemed to mostly be amongst the emperors and nobility. He likely would have become the chief god, replacing Jupiter/Zeus as king of the gods, but the rest of the roman cults would have remained most likely. Though Romulus likely would have declined in importance after the fall of the empire, or even after the move to Constantinople.

Another possibility considering evidence that Constantine actually used his own face in statues to Sol before his conversion, and afterwards included Sol in depictions of God and Jesus, its possible without Christianity he may have just declared himself Sol and the Roman Empire would have a system similar to Egypt in that the Emperor was Sol.