1) What is the opinion of people on this site of the validity of this idea in general?

2) The positive energy in the form of matter is supposed to be exactly or nearly exactly canceled out by the negative potential energy in the form of gravity. What about electrical potential energy though, doesn't this also factor in? If not, why?

And

3) I read somewhere that observationally, the 3-d metric of space is found to be very close to flat, which supports the zero-energy model, but the 4-d metric is supposed to be curved. Is this true? Does this refer to perhaps a negative curvature of Minkowski spacetime? How does that play into the zero-energy universe model and, also, how is dark energy supposed to fit in?

I think it depends on a particular definition of "energy", which has issues; in fact, *any* definition of the term "energy" that tries to give it a global meaning (which this one does) has issues in GR. In certain spacetimes, the issues can be resolved in a fairly reasonable way; but the spacetime that describes the universe as a whole is not such a spacetime (the main reason is that the universe is expanding).

It's part of the "positive energy in the form of matter"; "matter" in this particular case includes radiation, EM fields, etc.--basically anything that isn't gravity.

Yes; more precisely, it is found to *be* flat to within the accuracy of our current observations. But note that this depends on how we choose to slice up spacetime into space and time: see below.

Not really; you can construct a "zero energy" model of the universe regardless of its spatial curvature.

Also, the curvature of 3-d spatial slices depends on how you "cut" them out of 4-d spacetime. The slices that are found to be flat, to within the accuracy of our current observations, are slices cut in a particular way that makes the universe appear homogeneous and isotropic. There are good reasons why we use this particular slicing in our models, but that doesn't change the fact that other slicings, with non-flat spatial slices, are possible.

Yes. *Any* 4-d spacetime that has matter (in the general sense I referred to above) present *must* be curved, by the Einstein Field Equation.

No, because there is no such thing as "negative curvature of Minkowski spacetime". Minkowski spacetime is flat (4-d flat), by definition: that's what "Minkowski spacetime" *means*.

It doesn't, really; as I noted above, any 4-d spacetime that has matter present must be curved (4-d curved).

Dark energy is basically treated as a kind of "matter" (in the generalized sense I gave above), which happens to have some peculiar properties not shared by other kinds of "matter". This is true in basically any cosmological model, whether it claims to be a "zero energy universe" one or not.

Thanks peter, that is exactly what I was looking for. As far as your comment above, does that mean that there is postulated corresponding negative potential gravity that exists to counteract the dark energy as well as "traditional" forms of positive matter-energy? If so, wouldn't that mean that the vast majority of gravitational energy in the universe exists to counter this dark energy?

Actually, I'm not sure, because dark energy doesn't produce attractive gravity the way ordinary matter does. I didn't really take that into account in my previous post. Dark energy still has positive energy density, like ordinary matter does, but unlike ordinary matter, it has negative pressure, which means the net gravitational effect of dark energy (which depends on both energy density and pressure) is repulsive, not attractive.

Taking this into account, I'm not sure that a model including dark energy can have a negative "gravitational potential energy" that offsets the positive dark energy density, the way you can do that for ordinary matter. So I'm not sure there can be a "zero energy universe" model including dark energy. I would need to take some time to look at the math.