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The way I have heard it explained is that the universe creates its own space which it expands into.
It's not a bad explanation, though I do try to discourage taking it too seriously for a few reasons. It raises some difficult questions that do not have meaningful or testable answers. Like, "where does that new space come from, or where does it vanish to if the universe is collapsing?" I think it also can produce the wrong visual intuition for what's happening. When I hear it, I think "okay, imagine the universe is a sphere expanding into nothingness, and it is creating space at the edge of itself so that it can expand into it."
And that is 100% not
how it works.
It is better, at least in my own opinion, to refer to it as "metric expansion" and then explain what metric expansion means and where it comes from. Or if metric expansion is too technical then we can simply say expansion, or stretch, or whatever. They're just words. The observable effect
is that the distances between a collection of free particles increases.
Of course the question still stubbornly persists: "from where does this extra distance come from?" Well, it comes from the same thing that causes the distance between something you drop and the ground to decrease. You don't invoke space being "destroyed" to explain why an object falls towards Earth. In Newtonian mechanics you explain it with a gravitational force. Then in General Relativity you throw out the force and refer instead to space-time.
General relativity's description of space-time is the key to understanding cosmic expansion (we can also still usefully refer back to Newtonian mechanics and forces to describe it, though it won't be perfect). In the general relativistic context, the presence of matter and energy change the shape of the space-time, determining the path that you will follow if you are in freefall. Space-time tells mass how to move, and mass tells space-time how to curve. For something dropped near the Earth, the freefall path is towards the center of the Earth. Inside a black hole, every
allowed path goes inward. And for a universe uniformly filled with matter and energy, everything spreads apart by the inertia from the Big Bang, but the gravitational attraction of matter tries to bring them together, and dark energy drives them faster apart. The expansion of the universe can be understood as the path things take through space-time in exactly the same way that a dropped object falls to Earth because of space-time geometry around the Earth.
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Haha you got me thinking about the shape of the universe. Is it a torus?
Nope! The universe can be closed on itself, but it cannot be like a torus. (A shame; it would be very cool if we lived in a donut universe).
The reason is that on a torus, the distance you must travel to return to your origin is different depending on which direction you go in. But that would contradict the principles of isotropy and homogeneity for the universe -- the space cannot be shaped that way because it does not match the symmetries for how matter is distributed. If the universe is closed, then the distance to where space has curved back on itself (what I have loosely called the "curvature horizon" in previous posts) must be the same in any direction you pick, or from any starting location.
Because the universe is homogeneous and isotropic, general relativity only permits three possible shapes for it:
- Spatially Flat: If the total mass density equals the critical density (which it does, to within current precision of measurement), then the space is everywhere 3D Euclidean (what we call "flat"). In this case straight parallel lines remain parallel forever when extended, and the sum of angles in a triangle is always exactly 180°. Such a universe is also infinite in spatial extent, never curving back on itself. You can travel in any direction infinitely far and never return to your origin.
- Positively Curved: If the total density is greater than the critical density, then the space curves back on itself. Move far enough in any direction, and you will return to your origin (ignoring the effects of expansion which could prevent that.) Sum of angles in any triangle is greater than 180° and straight, initially parallel lines will converge. It is exactly the 3D analogy to the surface of a sphere. We could call it a hypersphere.
- Negatively Curved: Final case, if the total density is less than the critical density, then space is warped in such a way that the sum of angles in a triangle is less than 180°, and straight, parallel lines diverge from one another. A visual analogy is the region around a saddle point, where the surface bends upward along one axis and downward in the other. Except now try to visualize that property everywhere and in 3D. We can describe this as being a hyperbolic geometry.
The 2 dimensional analogues are illustrated here. Again a universe being "flat" doesn't mean it is like a pancake, but rather flat in 3 dimensions, which is simply the 3D Euclidean space that we are familiar with. Curved 3D spaces are hard to visualize.
Is it possible for us to measure the true shape of the universe? Yes, actually! The triangles in the above sketch illustrate the idea. By measuring the angular size of the fluctuations in the CMB, we are essentially "making very big triangles" through the universe, which in turn tells us its geometry. Specifically, this is the measurement of the "CMB angular power spectrum" I described on the previous page. The observations indicate that the space is very close to flat, with a precision of something on the order of 10%. Another way to test for curvature is to check the total mass density of the universe and compare to the critical density. Again if they are the same, then space is flat. If greater than critical, then positively curved, and if less than critical, negatively curved. Constraints on the mass density tell us the universe is flat to within about 2%.
What do these constraints tell us about how much space can curve back on itself (or away from itself, in the case of negative curvature)? The Planck 2015 observations indicate the total density parameter is Ωtotal = 1.0023, with 1-sigma error bars of about .0055. So let's look at the values 1.0023 (best estimate), 1.0078 (68% confidence it's less than that), 1.0133 (95% confidence), and 1.0188 (99.7% confidence). For each of these cases, what is the proper distance to where space starts curving back and distances start decreasing again?
= 1.0023, it comes out to 471GLY. If you could freeze the expansion and travel that far in any direction, you will then start to get closer to Earth again, just as if you went half-way around the world.
= 1.0078, this distance is reduced to 256GLY.
= 1.0133 it is 196GLY,
and finally for Ωtotal
= 1.0188 (99.7% confidence it isn't that large), it becomes 165GLY.
All of these distances are several times larger than the proper distance to the edge of the observable universe. So if the universe does curve back on itself, it must do so over much greater distances than what we can see. (Otherwise, of course, we would see it already.)
It is also over much greater distances than you can ever hope to travel (unless somehow we learn to go faster than the speed of light, and I am not holding my breath for that.) The distance to the cosmic event horizon was only ~16GLY! So we can safely conclude that even if space is curved in this way, we still cannot hope to travel out in a straight line and get back to where we started. Sad.
Now, I focused on the possibility that the total density was greater
than the critical density. If it is instead equal or less, then space isn't closed on itself at all. Better future measurements of the density of the universe and the curvature may constrain it to be closer and closer to the critical density (no curvature), but can never exclude the possibility that it is curved at least a little bit. It's sort of like how if we lived on a perfectly smooth sphere, then the larger the sphere is, the harder it is to measure the curvature. If it's really
large, then it just looks flat. Hence the Flat Earther's out there... (maybe they need to update to being Flat Universer's).