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We say the universe is expanding, and by expanding we mean the distance between objects gets larger over time. We call that "Metric Expansion of the Universe". So far so good. I kind of get the idea about of distances getting larger.

Now, I think of a balloon's surface and the distance between two arbitrary points on the surface gets larger as the metric expansion happens. But, in order for metric expansion to happen, doesn't the universe really expand INTO something. Balloon's surface expands into air so there's no problem imagining it, but how about the universe itself?

Also, do we mean the whole universe or observable universe when we say the universe is expanding? Both maybe?

Edit: Also, I know some multiverse theories that try to explain it, but the idea of universe is expanding has been there before multiverse was even considered, so I guess it can be explained without multiverse theories.

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    $\begingroup$ possible duplicate of If the universe is expanding, what is it expanding into? $\endgroup$
    – John Rennie
    Commented Feb 6, 2014 at 10:42
  • $\begingroup$ This also covers related ground: Whats left at the center of the Universe after Big bang? $\endgroup$
    – John Rennie
    Commented Feb 6, 2014 at 10:44
  • $\begingroup$ Anna's answer at the 'possible dublicate' thread is just what I've asked, so it's not literally an answer. She talks about the balloon analogy and I asked we can't really compare balloon and the universe.( Though the analogy itself is to only simplify the things for average people) The other one is merely about the center of universe and I don't claim the universe has a center! Thanks for the reply! $\endgroup$
    – user34284
    Commented Feb 6, 2014 at 10:50
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    $\begingroup$ Read the other question more carefully. It makes the point that if the universe is infinite it was always infinite. There is no outside for the universe to expand into because the universe fills everything. The balloon analogy falsely gives the impression that there is some dimension external to the universe. This is not the case. $\endgroup$
    – John Rennie
    Commented Feb 6, 2014 at 10:52
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    $\begingroup$ See also Universe being flat and why we can't see or access the space “behind” our universe plane?. $\endgroup$
    – John Rennie
    Commented Feb 6, 2014 at 10:56

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The balloon analogy is useful in some respects, but it is misleading in one important respect. In the balloon analogy the curavture of the balloon surface is extrinsic while in GR the curvature of the universe is intrinsic.

Extrinsic curvature is easy to understand. The surface of a balloon, or the hills and valleys on a landscape, or (to make a 1D analogy) a railway line are extrinsically curved because there is another dimension external to the surface that allows the surface to curve. We say that our surface is embedded in a manifold with a dimensionality one greater than the surface.

Intrinsic curvature is much harder to understand because it's counter intuitive. I described intrinsic curvature in my answer to Universe being flat and why we can't see or access the space "behind" our universe plane? but let me try a simpler example.

Suppose you watch an ant walking along an elastic rope, and you see the ant changing speed. You would assume the ant is accelerating. But suppose we had stretched some bits of the rope and compressed others:

Ant on rope

The dotted lines show equally spaced divisions on the unstretched rope, so when we compress the rope the dotted lines get closer together and when we stretch the rope the dotted lines get farther apart.

The key feature of intrinsic curvature (and GR) is that the ant sees all the divisions as equally spaced no matter how much we stretch the rope. So if the ant crawls one division per second on the unstretched rope it still crawls at one division per second on the stretched rope. So we see the ant moving more slowly at the left end of the rope than at the right end, and we might explain this by saying the ant is being accelerated by some force (like gravity). But actually the ant is moving in an intrinsically curved space.

This is what happens in GR. The curvature of spacetime is like some bits of spacetime being compressed and other bits being stretched, and this is what causes the acceleration that we describe as gravity. There is no external dimension that the universe is being curved in.

You started off by asking about the metric expansion of space. Well this is like the elastic rope being continuously stretched, but the rope is infinite and has no ends. So the rope isn't being stretched into anything - all the stretching is internal. Likewise the universe isn't expanding into anything.

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  • $\begingroup$ How can one stretch the rope without stretching the ant ? (Anlaogy of expansion of space) Expansion of universe says ohejcts at different distances observe different expansion ! If two equally spaced points experience some expansion then all of them will experience the same expansion amongst along with the ant ! How can you stretch just one side ? $\endgroup$
    – Rijul Gupta
    Commented Feb 6, 2014 at 14:52
  • $\begingroup$ @rijulgupta: I'm not sure what you're asking, but I suspect you might be pushing the ant/rope metaphor a bit far. Maybe you could rephrase your question to one about GR and ask it as a new question. $\endgroup$
    – John Rennie
    Commented Feb 6, 2014 at 14:59
  • $\begingroup$ your answer is good, and all I was saying (not asking) was that you have stretched only one side of rope ! Space expansion says every two points at same distance experience same expansion ! So you cant arbitrarily expand equal divisions of one side, all divisions must suffer equal expansion. $\endgroup$
    – Rijul Gupta
    Commented Feb 6, 2014 at 15:17
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    $\begingroup$ @rijulgupta: The rope diagram isn't meant to show the expansion of space. It's more like the change in curvature we get near a heavy object like a star. $\endgroup$
    – John Rennie
    Commented Feb 6, 2014 at 15:33
  • $\begingroup$ I know this is old but I stumbled across and your explanation of extrinsic and intrinsic seem to contradict this definition. Based on that definition, the property of intrinsic versus extrinsic isn't about whether the curvature is embedded in a higher dimension, it's whether you can observe it from 'within'. Your ant analogy suggests that intrinsic curvature is not observable which is the opposite. Is the wolfram definition incorrect? $\endgroup$
    – JimmyJames
    Commented Feb 8, 2022 at 17:37