Elasticity of Space; How does the expansion of Space affect gravity?

Does space have an elastic quality?

What I was thinking about was if space is expanding, is it being 'stretched', like a balloon being blown up, and if so, is this causing gravity to weaken? Imagine space as a 2 dimensional sheet (got this from one of Brian Greene's books) with planetary bodies resting on it and causing a depression in it, if you were pulling this sheet from all sides over a period of time, you would cause the depression of the planetary body to decrease and eventually become flat, which if we go back to reality, would mean that the gravitational 'constant' had changed to the point where the planetary body had no influence on those objects which were previously orbiting around it (or even residing on it's surface).

Is this the case in reality? Or does space not have an elastic quality? If not, can you explain to me what exactly it means for space to be expanding?

In case you didn't notice, I'm a layman (hence the Brian Greene books :p), so try to keep your answers/explanations conceptual if possible.

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You are a victim of the rubber sheet. Space is not a fabric or a rubber sheet, and to say it is "expanding" just means everything is moving away from everything else. – Ron Maimon Dec 26 '11 at 3:13
Could you go a bit further with your explanation? Surely if everything was "just moving away from everything else" and space has an enclosed shape (like a sphere or donut or whathaveyou), everything would also be moving toward each other, therefore 'something' must be expanding, and if it's expanding, is it being stretched, or is new space just being 'created'? – machinemessiah Dec 26 '11 at 5:16
Ok--- space is not a material, it is a label. In the case of the universe's expansion, there is an edge to the universe, a black wall, and it is just moving away from us at the speed of light. So we are in a box that is in the shape of a sphere which is bounded by a black wall, and is growing at the speed of light. – Ron Maimon Dec 26 '11 at 10:02
I'm not sure I understand you here, surely if that were the case (that space had an edge that was moving away at the speed of light), there would be a center from which everything was moving away, which is obviously not the case, can you elaborate (again, sorry if I'm getting annoying) – machinemessiah Dec 26 '11 at 20:49
@machinemessiah: The edge is different for different observers, and everyone sees it centered at their own position at all times, so it is symmetrical. Whether it is an "apparent edge" or not remains to be established. It is not an apparent edge the way I see it, because it really is a boundary, it is consistent to say that there is nothing outside, and it is likely inconsistent to say that there is a unique extension to the outside. but it is an observer dependent edge, so that if you take a rocket to the edge assuming you wait until the edge stops moving (in the future dS), you can go past. – Ron Maimon Dec 27 '11 at 4:16

Does space have an elastic quality?

No it does not.1 You're taking the "rubber sheet" analogy too far. It's only meant to help you accept the fact that objects curve spacetime and that their motion is affected by this curvature. If you go any further into general relativity than that, the analogy breaks down. In particular, the rubber sheet analogy has nothing to say about the expansion of spacetime.

What it means for space to be expanding is simply that the distance between any two objects (which are not bound together by some force) grows with time. You can find further explanation of this point in another answer I've written and some of the other answers to that question.

1To be fair: perhaps somebody has proposed a theory about elasticity of space, but if so, the idea has not caught on.

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Thanks David, I think I definitely have a habit of taking thought experiments too literally and using them to think about things outside of their immediate usefulness, probably due to a lack of formal education in the field. I think some further reading is required on my part to understand these things without requiring the misleading metaphors. – machinemessiah Dec 26 '11 at 20:44

I remember that Prof. Susskind said in the cosmology course of his "Stanford ongoing studies series" (it must have been somewhere in the first part of this 8 Lecture course)

http://www.newpackettech.com/Resources/Susskind/PHY28/Cosmology_Overview.htm

that space is continuously created in the course of the expansion such that the energy density keeps constant. This can be described by Hook`s law with a negative spring constant but it is not really a "rubber sheet". He mentioned to have derived a theoretical model to describe this process which is called "Newton Hooke cosmology".

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