What is meant by positive and negative gravity/energy/spacetime-curvature? I have recently come across some cosmological assertions (based on empirical data) about the universe being self contained in the sense that it is entirely capable of coming into existence from a zero-energy initial state. This is based on the observation that at grand scale the positive and negative gravity/energy etc. cancel out each other.
What do the terms positive and negative actually mean in this context?
 A: This is a very misleading claim which keeps being touted in popular science books and the media.
I asked about this earlier over here.
Total energy of the Universe
From what I can see, there is a lot of controversy over what total energy even means in the context of general relativity, so claims about "negative energy of gravity" balancing the positive energy of matter are basically vacuous.
A: 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?
A: I don't really have the background to understand such matters, but this presentation by Alan Guth gave me at least some idea of what it means to say the energy of a gravitational field is negative (which Guth calls a "miracle of physics").
Starting at 0:52:00 in that video clip, Guth presents this thought experiment...

...where it's taken as a given that there's no gravitational field (and hence no gravitational energy) inside a "hollow shell of mass". Guth then postulates arranging pulleys outside the shell, and having the shell shrink, so it encloses a smaller volume.
If those hypothetical pulleys were coupled to dynamos, they'd generate energy from the "collapse". So in the third diagram above, since the space between the original and final (now smaller) enclosed volume does now contain a gravitational field, and since the whole thought experiment is a "closed system" within which total energy remains constant, the (positive) energy "extracted" from the process must equal the (negative) energy of newly-present gravity in the shaded volume above.
That explanation works for me.
