# Expansion of the Universe

1. Jul 27, 2009

### TheIsland24

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. Jul 27, 2009

### sylas

Expansion is not a force. It's just the movement of things apart from each other. If there was no gravity, then expansion would continue at the same rate... analogous to movement of particles at constant velocity.

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. Jul 27, 2009

### negitron

You are.
Gravity acts to slow the expansion, that is to say it decelerates it. The decrease in gravity due to the lower density means only that the rate of the acceleration of the expansion will decrease. In order for the acceleration to increase, a force must apparently be at work. We currently call that force "dark energy" but we are really only just beginning to understand it.

4. Jul 27, 2009

### negitron

*shakes fist at fast-typing sylas*

5. Jul 27, 2009

### nutgeb

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 mass-energy 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 ever-declining 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.

Last edited: Jul 27, 2009
6. Jul 27, 2009

### TheIsland24

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. Jul 27, 2009

### sylas

Uh... nutgeb described near the end of his post the same effect of gravity on expansion that everyone else did. Gravitation attraction of matter retards, or slows, the rate of expansion.

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. Jul 28, 2009

### Chalnoth

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 space-time 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. Jul 28, 2009

### sylas

Yes and no. The term "matter" is more limited than the term "energy". For example, radiation is not a "different form of matter", but you could call it a different form of energy. That's my one quibble here.

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 co-moving 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. Jul 28, 2009

### Chalnoth

I wouldn't agree with that. Photons are as much matter as electrons. It's just that we mean something specific when we talk about "normal" matter, which means non-relativistic fermions. Basically, I take issue with a definition of matter which excludes things like electrons and protons that are traveling too fast.

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.

This isn't strictly accurate. The cosmological constant is one specific proposal for dark energy. There are others, though they all behave similarly at late times.

For example, so-called "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. Jul 28, 2009

### Ich

If we call anything with $$\rho > 0$$ "matter", as Chalnoth obviously intended, all possible variations follow the same law, dE=-pdV:
$$\frac{d}{d t}\,(\rho\,a^3) = -p\,\frac{d}{d t}\,(a^3)$$
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. Jul 28, 2009

### sylas

Terminology... I think the standard definition of "matter" is stuff that has non-zero rest mass. This excludes photons. But it is a terminology point.

I certainly don't exclude things on the basis of velocity. By my usage, which I think is pretty standard, the term matter excludes photons, but not relativistic protons or other particles with a non-zero rest mas. I noted explicitly that relativistic particles have an equation of state similar to photons.

By normal usage, energy is a property of more than only matter... and dark energy is basically a property of the vacuum.

Granted. I was simplifying a bit... deliberately, I confess. But I think we are on the same page. I'm just clearing up how we use terms.

Cheers -- sylas

13. Jul 30, 2009

### LtDan

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, what-have-you --- 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 red-shifted 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. Jul 30, 2009

### Chalnoth

The big bang theory, properly understood, does not include a beginning. It is generally recognized that the theory breaks down before you go that far back, and a different theory is needed to explain what happens at the earliest times. We don't yet know for certain how our region of the universe began, though the theoretical evidence indicates rather strongly that it had to begin at some point (though possibly from a pre-existing space-time).

That's not what the big bang theory says, though.

This is a pretty good analogy for what the big bang theory actually says.

Neither is necessarily the case. Our universe may be finite in size. It may be infinite. We don't know. Our region of the universe is almost certainly finite in age, but we don't know how old what it stemmed from is. That may be infinite in age. Or our region of the universe may have been what started it all off. We just don't know.

Well, that won't happen. They'll just get gradually more and more redshifted. They only reach zero brightness as time goes to infinity. There's no point where you could say, "after this time, these objects are no longer visible."

15. Jul 30, 2009

### LtDan

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. Jul 30, 2009

### Chalnoth

We can never see the photons that leave it after a certain time (not simply given by its recession velocity, but instead by the future expansion history of the universe). But this doesn't mean that we cease to see it: we see its after-image forever. It just gets dimmer and dimmer. And, as near as we can tell time slows and slows for this image as time goes forward, and the apparent age of the object in our after image asymptotically approaches the age at which the object crossed our horizon.

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. Jul 31, 2009

### LtDan

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

18. Jul 31, 2009

### Chalnoth

future expansion history = the way the universe expands into the future.
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.

19. Jul 31, 2009

### LtDan

Is it accurate to refer to our hypothetical infinite-aged and infinite-sized universe, operating in a "rising raisinbread" mode, as an "accelerating universe"?

Since our infinite universe has no outer edges, how can we judge the speed of the universe's expansion. One way would be by calculating expansion speed from the red shift observed in distant objects. Another would be by taking a chunk of the universe --- a chunk with observable edges to it --- and somehow measuring the speed at which that chunk of matter is expanding in size. Since all matter, both visible and invisible, is expanding in size at the same universal rate, it is impossible to measure any universal expansion growth against a constant measuring stick. The measuring stick is also expanding. The only way to discern and measure the expansion of our reference chunk is by referring to what we have been calling "gravity" since Newton's time.

The planet Earth is the handiest corporeal chunk of the universe to use in this exercise. It is expanding at a rate that causes objects located against it to stick to the planet's surface and to display the characteristic we call "weight."

Since the weight of such an object does not change from one second to the next, is it reasonable to assume that the outward movement of the Earth' surface is actually accelerating and not merely moving outward at a steady rate of speed? A steady rate of speed would seem to suffice to keep the planet in contact with its "companion," as long as the companion kept still. But if the companion were to, for instance, jump up in the air, there would seem to be nothing to prevent the companion from simply flying away. There would be no way for the planet's surface to catch up with the companion.

[In an old radio routine, Edgar Bergen was attempting to explain gravity to Mortimer Snerd. He asked Mortimer why, when he jumped up into the air, he returned to earth. Mortimeer replied, "I live there."]

Last edited: Jul 31, 2009
20. Aug 1, 2009

### Chalnoth

Yes, because the measured rate of expansion is accelerating.

Well, no, the measurement of the rate of expansion is largely independent of the behavior of gravity.

The Earth isn't expanding.

Ugh. You seem to be confusing the equivalence principle with actual acceleration. While a the existence of a uniform gravitational field is indistinguishable from acceleration, this does not mean that a gravitational field is acceleration. In particular, the gravitational field of a body like the Earth is not uniform at all, but changes from place to place (that is, it gets weaker as you move away from the Earth, and changes in direction as you go around the Earth). Because the gravitational field changes from place to place, there is no acceleration which can mimic the entire gravitational field. So the gravitational field of the Earth cannot be considered an acceleration.