No answer I'm afraid but I'd add my naive request to that of Mumtaz. It's true that I did hear this "negative energy" claim from a popular science TV program but since it was made by Stephen Hawking himself one cannot dismiss it. He seemed to suggest that in the co-emergence of space and mass-energy to form the universe, the space component embodied the negative energy required to balance the positive mass-energy component.
I find this difficult as I understand "space" to mean separation of material bodies, which under the attractive force fields (gravity, strong and weak nuclear forces etc.) represents positive potential energy (give or take a cosmological constant).
Perhaps Hawking means that potential energy in space thus affords a sink of kinetic and radiant energy and might thus be described as a negative energy reservoir. The "out of nothing" condition would imply however that this reservoir can be somehow be exactly filled by absorbing all kinetic and radiant energy in a final state of separation. Such a theory should surely have something to say about the approach to that endpoint. Does it?