Note that the zero-energy universe is highly speculative; in particular there is no good way to define the total energy confined to a volume at large scales and

Note that the zero-energy universe is highly speculative; in particular there is no good way to define the total energy confined to a volume at large scales and it's hard to say that "energy is conserved" in any way that's nontrivial. (A ready example is the apparent loss of energy in the redshifting of light due to Hubble expansion.)