# If the universe is expanding more rapidly now

1. Jun 15, 2010

### zewpals

Then what is the acceleration rate currently, what has been the change and will be the change in acceleration, and most importantly...

If it's still accelerating...wouldn't the universe's expansion have passed the speed of light? (unless it's approaching that limit)

That's about it. Oh. If it's not traveling faster than the speed of light, what is stopping light from going beyond the universe? Thanks!

2. Jun 16, 2010

### Chalnoth

Expansion isn't a speed. It's a rate. What's being talked about here is the time rate of change of the scale factor, and that can increase as much as you like, but it can't ever be greater than the speed of light in the same way that 3000rpm isn't greater than 30mph (the comparison doesn't even make sense).

3. Jun 16, 2010

### Dmitry67

But your intuitive idea makes sense - in fact, in accelerating Universe distant parts begin to recede so rapidly, that light from such areas will never ever reach us. This is called a 'cosmological horizon'

4. Jun 16, 2010

### Ich

Don't know which answer you expected or even if you're sure you want to ask about the acceleration rate, but here you go: It's currently 0.003 / Gy². It was zero some 6 Gy ago. It will be 0.004 / Gy in the distant future.

(Gy = billion years)

5. Jun 16, 2010

### zewpals

Haha Ich. Well at least that answer gave me numbers go with. Thanks for clearing that up Chalnoth. I'm still having a little difficulty comprehending the difference, but it'll click eventually.

6. Jun 26, 2010

### Kynan

Can you explain this a little further..
The way i'm picturing it is like driving a car.. you can drive at a constant speed or velocity... or accelerate.
So i understand how you can be accelerating at 5km/h and be going 100km/h and thus the two are incomparable.
But what I took from this question is what is causing the acceleration or change of rate to fluctuate?

7. Jun 26, 2010

### Chalnoth

Well, an acceleration is also not a speed. It's a change in a speed over time, so the units might be, say, 5km/h/h (which would mean that after an hour with that same acceleration, your speed would change by 5km/h).

Well, I think that's a somewhat different question, but the short answer is the interaction between gravity and the contents of the universe. If the rate of expansion doesn't change how we think it should, then this obviously means that either we understand the contents of the universe incorrectly, or we understand gravity incorrectly. Most people tend to think it a bit more likely that we're misunderstanding the contents than gravity in this case, because mathematically it's very difficult to produce a theory of gravity that produces such an acceleration but wouldn't already be measured experimentally.

8. Jun 26, 2010

### Kynan

9. Jun 26, 2010

### Chalnoth

Well, yes, this was discovered some time ago. The prevailing hypothesis, at present, is that the accelerated expansion is caused by a very small, but non-zero, cosmological constant.

You may be able to grasp how this works by considering the first Friedmann equation, which can be written as:
$$H = \sqrt{\rho}$$

Here $H$ is the Hubble parameter at a given time, and $\rho$ is the energy density of the universe. The Hubble parameter is defined as:

$$H = \frac{1}{a}\frac{da}{dt}$$

That is, it is the time rate of change of the scale factor $a$ divided by the scale factor. This parameter has the meaning that if we take any two galaxies and compute their distance, then the two galaxies will be moving away from one another at a speed $v = Hd$.

Now, if our energy density of the universe is constant, what does this mean?

$$H = const$$
$$\frac{1}{a}\frac{da}{dt} = const$$
$$\frac{da}{dt} = const*a$$

So we have a very simple differential equation, where the rate of change of this scale factor is proportional to its value. This is the equation for exponential growth.

One way to think about it is by looking at your bank account. Let's say that your bank pays you 5% interest per year. This means that the amount of money added to your account is proportional to the amount of money in the account. So the first year 5% is added to, say, $100, so you have$105. The second year, 5% is added to $105, so you have$110.25. Each year, the 5% adds a little bit more money, because you have a little bit more in the account. The amount of money in your account might be said to accelerate.

This is what's happening here: if, when we remove all matter, all radiation, all everything from a region of space, and still have some energy sitting around, an energy that is just a property of the vacuum itself, then that energy will be a constant, independent of the expansion of space. This sort of energy would cause an expansion that is proportional to the rate of expansion, and so the expansion accelerates with time.

Now, so far, this is highly speculative. We don't really know what's causing the expansion. But this is one plausible cause.

10. Jun 27, 2010

### Kynan

That is really well explained Chalnoth.
I appreciate it when someone goes to such detail to explain things well.

So am I right in that what you described below is what they are calling "dark energy"? and this energy is believed to permeate all of space before the big bang such that meaning it is a constant and not changing with with the expansion of the universe or with any respect to time.

"We do not yet have a good theoretical understanding of the observations that the expansion of the universe, is accelerating again, after a long period of slowing down."

What I gather from this is that the expansion of the universe was slowing down at some point.. so like a deceleration? and then randomly begun accelerating again? have I misunderstood this statement? If the dark energy is a constant then what would cause these fluctuations?

11. Jun 27, 2010

### rwmp

OK this is where I become totally baffled by the explanations. I accept that the cosmological constant does fit the observations. What disturbs me about this explanation is that we are implying an infinite expansion in the amount of energy in the universe. The universe grows larger and more energy appears out of the vacuum causing the universe to grow larger faster causing more energy to appear out of the vacuum etc. Can anyone help me make sense out of this concept which just seems so disturbing to me.

12. Jun 27, 2010

### Chalnoth

This is one potential sort of dark energy, yes. Any dark energy model ends up being very similar, however, in that it must permeate all of space and vary at most extremely slowly with time.

Well, yes, in the distant past, our universe was most definitely decelerating. This is what happens when you have a universe that is dominated by either radiation or normal matter. You can see this by examining the first Friedmann equation again:

$$H^2 = \rho$$

(note: I didn't mention this before, but I've dropped the constants in the equation for maximal clarity)

Where we also define:

$$H = \frac{1}{a}\frac{da}{dt}$$

If we are to have a deceleration, we want $da/dt$ to get smaller as the scale factor $a$ increases. If $da/dt$ gets smaller as $a$ increases, then this means that $H$ must get smaller faster than $1/a$. This means that $H^2$ must get smaller faster than $1/a^2$, and therefore the energy density of the universe must get smaller faster than $1/a^2$.

In other words, as long as you have an energy density that dilutes, and in particular dilutes faster than $1/a^2$, you get a universe that decelerates. In fact, this is exactly what happens as long as you have a universe that is made of nothing but matter and radiation. Normal matter, as the universe expands, just gets further apart. You have the same amount of mass in a larger volume. So normal matter dilutes as $1/a^3$: with normal matter you have deceleration.

With radiation, you get even more deceleration, because radiation not only dilutes in number, it also gets redshifted, so that radiation dilutes as $1/a^4$.

So basically the very early universe, when most of the energy was in radiation, was decelerating. But the radiation's energy dropped more rapidly than the normal matter, and so later on the normal matter ended up dominating the energy in the universe. The universe continued to decelerate, but more slowly. As time moved on, the normal matter continued to get more and more dilute, its energy dropping more and more, until the originally much smaller (but not decreasing!) energy density in dark energy came to dominate.

Now, today, the energy density of the universe is still decreasing, because the matter is still getting more and more dilute, but with matter already at only about 25% of the energy density and falling, the constant (or nearly so) energy density of dark energy has caused the expansion to accelerate.

13. Jun 27, 2010

### Chalnoth

Well, there are multiple ways to look at this. One is to point out that in order for there to be energy conservation, you need to have certain properties of the system in question that are constant with respect to time (See [URL [Broken] theorem[/url] for more, if you're interested). Energy conservation isn't a fundamental law: it only occurs in systems whose properties aren't changing with respect to time.

In the universe as a whole, the expansion destroys this time symmetry, and so you get no conservation of energy.

Now, even though you don't necessarily have energy conservation (depending upon the system), General Relativity does have some very strict conservation laws related to energy, momentum, pressure, and stress. It doesn't conserve any one of these quantities, but rather conserves a specific combination of them in what is called the "stress-energy tensor". It's not difficult to show that if you take matter that has some amount of pressure and put it in an expanding universe, the conservation of the stress-energy tensor forces energy to not be conserved. If the sort of matter has enough negative pressure, conservation of the stress-energy tensor forces the total energy in this sort of matter to grow with time.

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14. Jun 27, 2010

### rwmp

Thanks Chalnoth. I am still not comfortable with the explanation but you have given me a direction to go gather additional knowledge. If it would not be too much trouble could you explain how negative pressure occurs?

15. Jun 27, 2010

### Chalnoth

Well, the only way I know how to think of it is in terms of the cosmological constant. The cosmological constant is just a energy density that is a property of the vacuum. Keeping this energy density constant leads to a negative pressure when it interacts with the expansion (basically, gravity has to do work on the dark energy fluid to make it expand, because it has more total energy in a co-moving volume after expansion, which translates to having negative pressure).