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If there really is dark energy (the one that accelerates the expansion of the universe) shouldn't there be exotic matter too?
We don't really understand what dark energy is
, but it's a name we give to whatever causes the accelerating expansion that we observe. So it's like a placeholder name, which apparently has stuck. We say "energy" because whatever it is, it is uniformly distributed and does not dilute with expansion, which makes it act like an energy density associated with space itself rather than a distribution of matter particles. And we say "dark" because we don't detect it directly with electromagnetic observations.
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(The effect of both states (dark energy and exotic matter) is the same: antigravity.)
Now we get closer to the meat of your question: is dark energy like an antigravity, similar to exotic matter?
. Dark energy accelerates the expansion of the universe, but not by being repulsive!
Its mass or energy density is positive, so it's not like antigravity. But because it does not dilute with expansion, it generates a tension
pulling inward, rather than a pressure pushing outward. That probably still sounds very weird or even backward. You might think that pressure should help increase the expansion rate. But there are no walls, no edge of the universe for pressure to push against, so it doesn't help expand the universe at all. Instead, the pressure modifies the geometry of spacetime according to Einstein's general relativistic field equations, which in turn change the expansion rate, and it works out in the opposite direction of our intuitions. In cosmology, pressure slows expansion down, and tension speeds it up!
Example: in the very early universe when things were extremely hot, all the particles were moving around so fast that the pressure they generated was the most significant form of mass-energy in the universe. We call this the "radiation dominated era". That pressure slowed the expansion rate down even more rapidly than a matter dominated universe would.
see why this is and why tension should speed up expansion while pressure would slow it down, we need to go through some mechanics and derive the equations that describe how the expansion rate changes -- those are the Friedmann equations.
I've mentioned them before and still intend eventually to get around to writing a post for the cosmology thread to show where these equations come from and help demystify what they mean. They're quite possibly the most important equations in all of cosmology. But for now, I'll just say that it basically has to do with the laws of thermodynamics and the work done in expanding the contents of the universe. I promise that it all makes sense when we work through the details.
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But apart from that, would the so-called exotic matter really be needed to keep wormholes open?
Wouldn't dark energy also suffice for this?
Now we're there. "Could dark energy hold wormholes open instead of us needing exotic matter?"
Maybe! The dark energy could support the wormhole throat against collapsing, and there are some papers exploring that idea
, but as described above it would work in a different way than the "antigravity" of exotic matter. With dark energy we utilize the tension or negative pressure it produces. The trick, though, is that dark energy appears to be uniformly distributed in the universe and a property of space itself, whereas we imagine exotic matter (if it exists) as something we could either generate or gather and then distribute it in any way we want. Dark energy might have the right properties, but it's apparently not something that we can use to our benefit. It just... makes the universe expand faster.
I hope that's at least somewhat helpful an explanation -- these are pretty difficult and mind-bending concepts, as is par for the course when cosmology is concerned. I'm sure much may still be unclear, and if so please feel free to ask more questions!