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Expansion of the Universe 
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#1
Jul2709, 01:35 PM

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In "A Brief History of Time" Hawking questions why the expansion of the universe is accelerating. I must be missing something. If the universe is expanding, its volume is constantly increasing. If its volume is increasing its density is decreasing, so there is more space between bodies/particles and less gravitational force. The farther these particles get from each other, the less resistance there will be on the expansion of the universe...therefore causing it to expand faster and faster. What would have to happen to cause a Big Crunch? Would the rate of the creation of new particles have to be greater than the rate at which the universe was expanding? Help me Out.



#2
Jul2709, 01:55 PM

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With any gravity, expansion tends to slow down, because gravity pulls things together. But, strangely, things appear to be moving aprt from each other faster, and faster... as if something is giving them an extra boost. The "something" is called "dark energy". And we don't really know anything more about it than it is whatever it is that gives that bit of an extra push to make thing increase in the speed at which they are dispersing. The Big Crunch is an idea which applies if the force of gravity to pull things together is sufficiently strong to actually slow the expansion, or dispersion, and bring it to a stop, reverse it, and then start everything falling back together again. In terms of just two particles (rather than an entire universe of particles) it is analogous to the particles moving apart at less than escape velocity. They'll eventually stop, reverse, and start moving together. Same with a universe that has a "critical density" of mass and no dark energy. Cheers  sylas 


#3
Jul2709, 01:56 PM

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#4
Jul2709, 01:57 PM

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Expansion of the Universe
*shakes fist at fasttyping sylas*



#5
Jul2709, 03:01 PM

P: 294

There are two kinds of expansion:
1. The original expansion left over from the Big Bang (or inflation). This expansion acts like momentum, and is progressively slowed by the gravity of the massenergy in the universe. This expansion does not act like a force. It cannot cause objects to separate unless the objects were already separating in the initial conditions. 2. The more recent acceleration of expansion over the last 7 Gy or so caused by Lambda, Dark Energy, the cosmological constant, whatever you want to call it. This expansion does act like a force. It can cause objects to begin separating even if they were not separating previously. And if they were already separating (e.g. in the Hubble flow) it will cause the rate of separation to increase. Lambda is believed to impart sufficient acceleration to the expansion that the universe will never collapse in a Big Crunch. Instead, the expansion will continue accelerating until it asymptotically approaches the acceleration rate of Lambda alone, with the offsetting deceleration effect of gravity having become utterly insignificant, due to the everdeclining density of matter. Keep in mind that even if there were no Lambda, the universe would not necessarily have collapsed in a Big Crunch. That depends on whether the matter density was sufficiently high compared to the expansion rate (Hubble rate). Such a universe would eventually collapse only if it were "overdense", meaning that it was above critical density. A universe exactly at critical density (and without any Lambda) would expand more and more slowly over time; the Hubble rate would asymptotically approach zero, but would never quite reach zero in finite time. The Hubble rate would never go negative, so such a universe would not collapse. This decreasing rate of deceleration is due to the decreasing effect of gravity, which in turn is due to the decreasing matter density, as you allude to in your OP. But adding Lambda to the mix changes the situation. 


#6
Jul2709, 03:30 PM

P: 8

Thank you Nutgeb! That explained it. So gravity cannot affect the resultant expansion of the big bang. So are you saying that gravity does affect Dark Energy?



#7
Jul2709, 11:36 PM

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He also described the critical density case, where which is a case where the density is not quite enough to to reverse the expansion back to contraction. 


#8
Jul2809, 12:57 AM

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I think that talking about "dark energy" as if it's some force different from gravity is poor use of language.
General Relativity provides a connection between spacetime and matter. If you fill the universe with different sorts of matter, the expansion behaves differently. Fill it with normal matter, and it decelerates. Fill it with radiation, and it decelerates even more rapidly. Fill it with one of many types of hypothetical matter now placed under the umbrella term "dark energy", though, and it accelerates. It's still the action of gravity that is affecting the expansion, not some new force. It's just that gravity acts differently depending upon the properties of the underlying matter. The property in question that is important is the relationship between the density of the matter in question and its pressure. Radiation has positive pressure equal to one third of its energy density, and that positive pressure causes the expansion to slow more rapidly. Normal matter has no pressure (e.g. galaxies don't experience pressure between one another). To get acceleration, you have to have negative pressure that is more negative than minus one third the energy density. A cosmological constant, for instance, has negative pressure equal to the energy density. 


#9
Jul2809, 06:45 AM

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The key point is this. As the universe expands and disperses, the density of matter drops. The energy density of radiation (or matter at relativistic speeds, like neutrinos) drops even more quickly, because the cosmological redshift means energy density in a given comoving region reduces by an additional factor on top of the number density of particles. And finally, the "dark energy" term, also called "cosmological constant", corresponds to an energy associated with the vacuum. The density of this energy remains fixed; it is like a property of empty space. In general relativity, the crucial quantity is energy... whether it be in the form of matter, or radiation, or some energy associated with the vacuum. So there is indeed a strong sense in which dark energy is not an alternative to gravity at all. It's all still contained in the same relativistic account of gravity as the effects of matter. What changes is the way energy density varies with the dispersal of expansion of the universe; this is what is different from matter, and from radiation. Cheers  sylas 


#10
Jul2809, 07:06 AM

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The problem with calling these things "energy" is that energy in itself is a property of matter. It isn't something that exists on its own. For example, socalled "quintessence" models of dark energy track the energy density of the most dominant form of matter at early times (meaning that early in the universe, this "quintessence" matter dilutes just like radiation, later like matter). At very late times, when the universe is sufficiently dilute, it starts to approach a constant energy density. 


#11
Jul2809, 07:10 AM

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[tex]\frac{d}{d t}\,(\rho\,a^3) = p\,\frac{d}{d t}\,(a^3)[/tex] So I think it's ok to say that there may be all sorts matter or stuff or something with different equations of state, but all on an equal footing, as far as GR is concerned. But I think we all agree anyway. 


#12
Jul2809, 07:18 AM

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Cheers  sylas 


#13
Jul3009, 03:01 PM

P: 19

If the universe has always existed  is retrospectively infinite  then there was no "big bang" that started it.
If we hypothesize that is true, then the expansion of the universe which we observe happening is not an expansion outward from a single point of initial explosion. There would have been no such beginning point. Another explanation of the expansion is needed. Another type of expansion is the expansion that takes place with respect to a rising piece of bread dough. Visualize a lump of rising dough that has raisins scattered throughout it. As the bread dough expands under the influence of the yeast  aka dark energy  the raisins move farther and farther apart from one another. The further any two raisins are located apart from one another in the matrix of the dough, the faster those two raisins will move apart from one another, and their rate of separation will steadily accelerate. This seems analogous to what we are observing with our powerful telescopes. The farther things are away from us in space, the faster they are moving away from us (and us from them). It is as if the universe is structured very much like the raisinbread model. The "dough" is invisible and expanding "dark matter," and all of the corporeal structures imbedded within the dough  planets, stars, people, whathaveyou  are the raisins. The only two differences may be: (1) that the corporeal "raisins" in the real universe  what we call "matter"  also expand at the same rate that the doughy dark matter expands, so that relative near spatial intervals appear to us to be unchanging; and (2) that there is no limit  outer edges  of the universe, it being infinite in size as well as in age. I expect that the latest expansion of the Hubble telescope's visual accuity has revealed more and more "raisins" out beyond our previous limits of observation. I expect that they are more and more redshifted toward an ultimate point of invisibility where the separation rate between our planet and those distant bodies attains and exceeds the speed of light. Perhaps we are getting close to the point where we will be able to observe these distant bodies "wink out" of vivibility. 


#14
Jul3009, 03:34 PM

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#15
Jul3009, 04:24 PM

P: 19

If the rate of separation between Earth and a visible far distant object in space eventually reaches and exceeds the speed of light, wouldn't that far distant object become invisible to us?



#16
Jul3009, 05:24 PM

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Note, however, that this is only true in an accelerating universe. If the universe were not accelerating, or stopped accelerating at some point in the future, then there would be no future horizon, and, given infinite time, we would be able to see the full history of all objects in the universe. 


#17
Jul3109, 04:11 AM

P: 19

There are two terms I do not understand: "future expansion history" and "asymptotically."



#18
Jul3109, 06:21 AM

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asymptotically = behavior that a system approaches out to infinity. Hopefully future expansion history is understandable. Asymptotically may take a little bit more work. A simple example would be this equation: f(x) = 1/x. In the above equation, f(x) approaches zero as x approaches infinity. This is known as asymptotic behavior: there isn't actually any number x for which f(x) = 0. But as x gets bigger and bigger, f(x) gets closer and closer to zero without actually hitting zero. 


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