[VadeRetro]

How can one distinguish between an object's velocity (movement relative to space) from space itself expanding?

I think a clue was the way red-shift correlates with distance. Either we're really at the center of the universe and the whole thing is moving away from us or the whole blob is expanding and diffusing. The former position looks attractive to some people but there's a lack of corroborating evidence that our corner of the universe is that special.

Similarily, general relativity accounts for gravity due to space curving, but curving relative to what, meta-space?

You can see the curvature of space when dense foreground objects lens galaxies behind them, or the sun subtly shifts the apparent position (as seen from earth) of a star behind it. Thus, you can say "curving relative to less-curved space." At any rate, this action of mass on space is well documented now.

[Pres Raygun]

Thanks for the reply. I'm not doubting Big Bang Cosmology just trying to understand it better. Your answer to the first question is not completely satisfying. If the Big Bang was an explosion from a single point in space rather than expansion of space, then the observed increasing red-shift with distance would be expected, provided that the pieces continued to accelerate throughout the history of the universe. If this were the case, we would appear to be at the center of the explosion even if we were not.

Regarding the second question, I understand the overwhelming evidence supporting the curvature of space, but any curvature must be relative to some other geometry. I was just wondering how general relativity deals with this other geometry.