kk434":1vz4lfzy said:
The latest data says that ordinary matter is 4%, dark matter 23% and dark energy the rest (about 73%).
I understand that Dark matter is some kind of "matter", but why is Dark energy counted in the equation? Dark energy sounds more like a force (against gravity) and no one counts gravity as some kind of "missing mass". Is the LambdaCDM model messed up?
Dark energy isn't a force acting against gravity. It's all gravity. With normal stuff, gravity is attractive, but (see my post above) certain kinds of exotic stuff will make gravity repulsive.
(To be more mathematical: you can think of the cosmological constant in two ways. The first way is as a modification to Einstein's equations of general relativity describing how gravity works, by adding a new term in. But if you move that term to the other side of the equation, then you can just as well interpret it as a type of matter/energy, albeit a very bizarre one. However, that bizarre type of energy corresponds exactly to what we would expect from the quantum vacuum, a prediction from a completely separate branch of physics, which is suggestive.)
The numbers you've quoted are, as Chris mentioned, the density parameters for different contributions to the mass-energy of the universe, using the Greek letter omega. For things like matter and radiation, these measure density in spacetime. Even if you interpret the cosmological constant as an element of gravity, rather than a kind of stuff (which, as I said, are mathematically equivalent, so it's an open question as to whether those two scenarios are different at all), its value fits into the Friedmann equation - which governs how the Universe expands - in a similar way to the matter densities in the same equation, so we can define the "density" of those objects even if before it wasn't obvious how to do so. In the same way we're even able to talk about the density of spacetime curvature, which
definitely isn't a "stuff" which you can weigh in the same way as you can matter. But, from the way it tells spacetime how to expand, you can still figure out its density (which, incidentally, is almost certainly zero). Some of the mathematical details are here:
http://en.wikipedia.org/wiki/Friedmann_ ... _equations
csmyth3025":1vz4lfzy said:
As I understand it, various lines of evidence indicate that the overall curvature of spacetime in our observable universe is very nearly "flat" (like a sheet of paper) as opposed to being positively curved (like a beach ball) or negatively curved (like a saddle). I don't pretend to know what this really means, except that cosmologists say that in order for the geometry of the universe to be "flat", it must contain a certain critical density of matter/energy. The reason that energy is included is that energy possesses an equivalent mass according to Einstein's famous equation, E=mc^2. For the purpose of this calculation the preceding formula would be rearranged in order to give the equivalent mass thus: E/c^2=m.
If you set c=1 you don't have to rearrange anything, the formula's just E=m
Much less catchy, but makes things a bit more intuitive. And saves some writing.
Anyway, think of a balloon rising into the air. (This is not the same balloon which we put dots on and blow up as an analogy to the expansion of the Universe. This is a
completely different balloon. That balloon was red. This one is purple.) It's rising in the air, but you want to bring it down, so you tie a large rock to it. That sends it down. If you tied a pebble to it, it probably wouldn't have done much, though, the balloon would have kept on its merry way up. But there's some key rock weight that's right in the middle - when you tie it to the balloon it's not quite heavy enough to bring it down, but not too light to let it continue rising.
That's basically what the critical density is. Matter, as you know, curves spacetime. If there's a lot of matter, spacetime gets curved a lot - in fact, so much so that it becomes positively curved, or closed. Closed really just means that the Universe is like a 3-D version of the Earth's surface: if you go far enough one way, you come back the other side.
On the other hand, if there's very little matter, then the Universe can be negatively curved, or open. As Chris said, this is kind of a 3-D version of a saddle, but unlike the positive curvature case, where there's a 2-D analogue, there really is no 2-D equivalent of a negatively curved space that we can draw. The curvy part of a saddle is only a good approximation.
So, like Goldilocks, in order to have curvature right in the middle - corresponding to flat, like a 3-D version of a sheet of paper - the matter density needs to be right in the middle. There's only one density which will work, and that's called the critical density. Omega, the density parameter, is just the ratio of a particular density to the critical density. So, matter (dark and normal) has omega_m = ~0.3, so the density of matter is about 30% of the density needed to make the Universe flat. In fact, it was the observation that there wasn't enough matter to make the Universe flat, combined with the theoretical prediction (from inflation) that the Universe should be flat, that led some people to believe in the cosmological constant before it was detected.
Since subsequent observations have shown that the Universe is, in fact, flat (or very nearly so), this allows us to also say that matter comprises about 30% of the total stuff in the Universe. Luckily, when we discovered dark energy, we found that its density is just about that 70% necessary to close off the Universe. The evidence for dark energy (at least the initial evidence) and the evidence for the Universe being flat are pretty much completely independent, so it's comforting that they both point to the same conclusion to a fairly shocking amount of mathematical accuracy.
(Note: when I said "matter" above, I meant generically all forms of matter, energy, and the like. As far as gravity is concerned, they're the same.)
I don't know how gravity fits in to the whole energy thing when calculating "omega" (the ratio of the observed mass/energy in the universe to the "critical density" of mass/energy).
Chris
See above - for things which don't have an easily defined density, it's their contribution to the Friedmann equation - which comes from their interactions with gravity - which determines their share of omega.
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