I recommend that Big History expand its method to include the history of humanity's differentiating consciousness and reask the God question. The God Question turns Big History into Cosmic History.
One task of history within Big History, I believe, should be to chronicle and interpret leaps in consciousness. One leap of particular interest is the Axial Threshold. Unfortunately, this concern is not as central to practicing big historians as I would like to see. I think Big History should include history of consciousness.
Mitchell Diamond's critique of Ted Peters is actually a critique of Big History. Diamond argues that both morality and tribalism predated the rise of religion in evolution. Science needs to better explain religion's origin and persistence. Critique of Ted Peters