Questioning Zero Reference and the Expansion of the Universe

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I have a question about zero reference. Let us assume the expansion of the universe is due to the expansion of space-time. The analogy I have heard is sort of an expanding foam to account for the faster expansion of the perimeter. Here is the question, if we assume our Earth reference, within the middle of the expanding foam, is zero reference, does that imply the perimeter is heading toward negative reference? In other words, how can space-time continue to expand if it has already reach zero reference on earth. Does that mean we are not in zero reference?
 
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I guess anywhere is zero reference. An observer at the edge of our visable universe will consider us to be at the edge of their visible universe ("expanding" away from them) and consider themselves to be at the centre of their visible universe.
 
I'm not sure what you mean by "zero reference" or "perimeter", but it sounds as if you're thinking that the expansion occurs radially away from a central point. This is not actually the case, as I understand it. It's actually more of a uniform expansion where the distances between points grows equally in all directions. The analogy that is often offered is that of the surface points of a balloon as it is inflated. There is no central latitude/longitude point from which all other points recede. Of course, that's a 2-D example, and you have to extend that to 4-D, but you can do that, right? ;-)
 
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From $$0 = \delta(g^{\alpha\mu}g_{\mu\nu}) = g^{\alpha\mu} \delta g_{\mu\nu} + g_{\mu\nu} \delta g^{\alpha\mu}$$ we have $$g^{\alpha\mu} \delta g_{\mu\nu} = -g_{\mu\nu} \delta g^{\alpha\mu} \,\, . $$ Multiply both sides by ##g_{\alpha\beta}## to get $$\delta g_{\beta\nu} = -g_{\alpha\beta} g_{\mu\nu} \delta g^{\alpha\mu} \qquad(*)$$ (This is Dirac's eq. (26.9) in "GTR".) On the other hand, the variation ##\delta g^{\alpha\mu} = \bar{g}^{\alpha\mu} - g^{\alpha\mu}## should be a tensor...
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