# Question reguarding the expanding universe

1. Nov 2, 2015

### Daniel K

Hi.
I was recently researching the Hubble Sphere - a concept that is within cosmology - and someone claimed something interesting.
The individual contended that the universe has been decelerating since the big bang, and that the so called "acceleration" in the expansion of the universe is space slowing down in deceleration. This contradicts some of my previous studying, and I was thinking that one of you could clarify this subject for me.

2. Nov 2, 2015

### andrewkirk

It depends on what is meant by 'ac/decelerating'. See this thread that discussed this issue.
One way to express it might be that the Hubble Sphere is growing at a rate that is more than linear but less than exponential. So compared to a linear growth rate it is 'accelerating' whereas compared to an exponential growth rate it is 'decelerating'.

It is more usual in everyday speech to compare to a linear growth rate, so the former expression is more widely used.

3. Nov 2, 2015

### Chalnoth

The Hubble sphere is slowly shrinking, as the Hubble sphere is solely a function of the rate of expansion, which is slowly decreasing.

The accelerated expansion refers to the distances between objects: objects within our universe are moving away from one another at accelerating velocities.

4. Nov 2, 2015

### bapowell

The Hubble sphere grows as long as long as $w > -1$. Chalnoth, perhaps you mean that the Hubble sphere in comoving units is shrinking?

5. Nov 2, 2015

### Daniel K

so to clear up my confusion- the universe was expanding at its fastest when the Big Bang occurred, right?

6. Nov 2, 2015

### Daniel K

Additionally, even though the universe is accelerating in expansion, it's still decelerating? By this I mean that deceleration is still occuring, it's just happening at a slower velocity.

7. Nov 2, 2015

### marcus

Try this, Daniel:
focus on definite mathematically defined quantities. If someone tries to talk purely verbally don't listen, just skip what they have to say. Words are inherently vague and can throw you off badly.
Here's a history of the H(t), expressed as a percentage distance growth rate"
Code (Text):
year        fraction of percent expansion per million years
1 billion        1/15
...
...
11 billion      1/128
12 billion      1/135
13 billion      1/140
14 billion      1/145
15 billion      1/149
...
...
50 billion      1/173  (approx. equal to H∞ the longterm rate)
Our present-day growth rate in this year 13.8 billion is 1/144 % per million years

You can see it is tending to level out and in fact it is approaching a constant H. If you want I can attach a graphic plot.

Of course with a constant or near constant growth RATE, the growth of any particular distance between specified roughly stationary galaxies is EXPONENTIAL. So it will exhibit increasing speed of growth. Eg growing at 1/173 % per million years. I'm not concerned with that. I want you to understand the declining expansion rate. It has been declining ever since the big kick it got at the start, and it is gradually tailing off to H

That is what the Friedman equation says
H2 - H2 = [const] ρ
where rho is the combined ordinary and dark matter density. Matter density is declining so H is converging towards its longterm value H.
Present-day matter density expressed as energy equivalent per volume is 0.24 nanojoule per cubic meter. That's the same as 0.24 joule per cubic kilometer, which might be easier to imagine. A joule is enough energy to lift a 1 kilogram book up 10 cm. Or it's the thud when you drop the book back down on the desk.
The matter of all the stars, dust, gas, dark matter clouds, radiation, everything--in energy density units, averages out to this 0.24 joule per cubic km, or 0.24 nano joule per m3

If matter density is expressed in nanojoule per cubic meter, and H is in percent growth per million years, then the numerical value of the constant in the equation is 6.2×10-5 sometimes written as 6.2e-5

Here as a numerical check is the Friedman equation applied to presentday expansion rate (1/144 percent per million years) and presentday matter density.
1/1442 - 1/1732 = 6.2e-5 × 0.24

You can check the Friedman equation yourself, just put this in to google window
1/144^2 - 1/173^2 and press return. Google has a calculator and will tell you what the lefthand side is
And then put in 6.2e-5*0.24. Google calculator likes the asterisk for multiplication. It will tell you the righthand side. The two agree. That's the Friedman equation. (in the simple case where space, not spacetime however!, is flat, as it seems in fact to be)

You can play around with different times and different growth rates. You can use the equation to find out the density of ordinary and dark matter in year 1 billion, when H was 1/15%
Google calculator is very handy for this: Just paste in
1/15^2 - 1/173^2 to get the leftside and then divide by 6.2e-5 to get the rho on the rightside.
It will be a much larger matter density than the 0.24 we have now. Because a lot earlier.

The point about the rate tailing off to a constant is that to the extent that we have a constant expansion rate we have exponential distance growth at a constant percentage growth rate. So if you look at a specific distance between two essentially stationary galaxies, that distance is growing exponentially. The speed of distance growth, for that particular distance you are tracking, is of course increasing and naturally it is not limited by c because this is geometry change, not ordinary motion. Nobody gets anywhere by it, everybody just becomes farther apart. Not good to think of it as ordinary relative motion (which is limited by c.)

Last edited: Nov 2, 2015
8. Nov 2, 2015

### bapowell

Expansion does not proceed at a speed: it is a really a speed per distance. The expansion rate is given by the Hubble parameter, which is defined as the logarithmic rate of change of the scale factor, $H=\dot{a}/a$. You might be familiar with Hubble's Law, which says that the recession velocity of an object is proportional to its distance from us: $v_{rec} = Hr$. And so for a fixed rate of expansion, $H$, the recession velocity -- the speed at which objects appear to move away from Earth -- depends on their distance. When we say the universe is accelerating/decelerating, we are referring to the sign of $\ddot{a}$. If it's positive, then the universe is accelerating: objects recede from one another at an accelerated rate.

9. Nov 2, 2015

### marcus

Didn't see Brian Powell's post! I am partially repeating what you said, Brian.

The "speed the universe is expanding" is not defined. Different distances expand with different speeds proportional to their size.
So it useless to talk about it. Although many people talk in that vague way.
You only get a definite speed when you have picked two specific objects (individual motion negligible) and then the size of the distance between them is growing at some speed.
Speed, at any time, is proportional to size, so what is well defined is the percentage growth rate of distance. That is called H(t) and its development over time is described by the Friedman equation (a simplified cousin of the Einstein GR equation)

10. Nov 2, 2015

### Chalnoth

Sorry, yes, you're right. It does grow, as its radius proportional to $1/H_0$, while $H_0$ is shrinking. As $H_0$ is asymptotically approaching a constant value, however, this growth of the Hubble radius should be decelerating.

11. Nov 2, 2015

### marcus

Indeed! The Hubble radius is approaching a limit of 17.3 billion light years.
At present it is 14.4 billion LY, so it has a way to go still. The growth speed of that distance quantity is slowly declining.
In this table the age of expansion increases about 100 million years each step
$${\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}$$ $${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline S&T (Gy)&R (Gly) \\ \hline 1.000&13.787206&14.399932\\ \hline 0.993&13.887300&14.445708\\ \hline 0.986&13.987566&14.491047\\ \hline 0.979&14.088288&14.535790\\ \hline 0.973&14.189319&14.580014\\ \hline 0.966&14.290655&14.623720\\ \hline 0.959&14.392293&14.666909\\ \hline 0.953&14.494229&14.709581\\ \hline 0.946&14.596459&14.751736\\ \hline \end{array}}$$

And at first the Hubble radius increases by 0.19 Gly, or about 190 million LY, so speed about 1.9c
But by the end of the table the increase is only about 184 million LY, in about the same amount of time.
The speed of radius growth has declined. This is not a speed of MOTION, or of the expansion of a cosmological distance, but it is the speed of growth of a well-defined distance Δr/Δt

Last edited: Nov 2, 2015
12. Nov 2, 2015

### Daniel K

Thank you for responding guys. You've cleared a lot of points up for me although I'm still confused on a certain few.
So what I think you're saying Marus is that space expansion cannot be defined at a certain velocity; rather, only specific and definite objects can have their expansion rates measured relative to each other proportional to their amount of distance in between them.
Also, the rate at which two objects are expanding at the same distance away is now slower then what it used to be. This would explain why the hubble sphere is growing.
I'm sorry that I'm not catching on immediately - I have no back round in physics and I'm trying to familiarize myself with it.

13. Nov 2, 2015

### Daniel K

This is where my confusion stems from.

"So leaving Dark Energy acceleration aside for now, the essential fact of the size of the Hubble Sphere is that it expands when the overall expansion rate of the universe is slowing down.......and the overall expansion has been slowing down ever since the big bang when space and energy first burst outward. So the Hubble Sphere has been expanding in size relative to the rest of the universe over all of the age of the universe too.

That's the basic picture......and that was the total picture until 1998 when astrophysicists made a hugely important (2011 Nobel Prize winning) discovery that is usually just described in the popular science media as the ACCELERATION of the universe. Something called "Dark Energy" was theoretically postulated to explain it. On a surface level......for someone who knows that the universe has been slowing down and that the Hubble Parameter has been decreasing over all the age of the universe.......this is confusing. How can the universe be slowing down if the popular science headlines say that it's “Accelerating”?

On one level, you can just say that it's a form of acceleration that has the effect of reducing the rate of decline of the Hubble Parameter over time. But the Hubble Parameter is still declining and the Hubble Sphere is still expanding as before.......except just not as fast as they were before Dark Energy acceleration kicked in about 5 billion years ago."

14. Nov 2, 2015

### marcus

Right!

The whole content of the discovery was the the decline of H is not going to zero but is leveling out at a positive H.

This possibility was allowed for in Einstein original GR equation, the Lambda term appeared around 1917, there was no "dark energy". DE is a hyped-up myth that appeals to laymen, journalists, and some types of scientist. They keep looking for evidence that the positive longterm limit H (basically the cosmo const Lambda in disguise) arises from some sort of "dark energy". But they have failed for 17 years so far to find evidence. The behavior is still most simply explained by a positive Lambda constant in the equation. So its up to you, you can take part in the DE fantasizing or you can reserve judgement and go with the simpler explanation (until and if they find solid observational evidence for DE). It's kind of a matter of personal taste.

Longterm H equal to 1/173% per million years (see table post #7) is equivalent to saying
Hubble radius is increasing to a limit of 17.3 billion light years. Two ways of saying same thing.

Last edited: Nov 2, 2015
15. Nov 2, 2015

### Daniel K

THANK YOU SO MUCH I FINALLY UNDERSTAND IT

16. Nov 2, 2015

### marcus

My pleasure! Thanks for the persistent/thoughtful questioning.

17. Nov 2, 2015

### Daniel K

Okay so this is my very last question - also thanks for all the help. I really do appreciate it.

If I understand 100% correctly, the universe is decelerating. However recently the rate at which it decelerates is slowing down, and so a way the universe is actually accelerating. (Sorry if this seems counter-intuitive/confusing)

Scientists do not know why this acceleration happened - some posture that it's dark energy however many informed people about the subject disagree with them. (such as you).

Correct?

18. Nov 2, 2015

### marcus

People have different standards and taste about how they talk. For me, that way of describing the situation is to vague and verbal (as opposed to quantitative).
For me, some key words and phrases in a sentence should refer to definite quantities.
Otherwise the talk is merely verbal. not quantitative.

When you say something, you and the listener have to understand what quantities the words refer to. You have to be able to illustrate with actual numbers. You have to be able to say what is actually increasing and what is actually decreasing. Otherwise it is too vague and is likely to confuse people and not really mean anything.

If you are talking with a friend and trying to be clear about what is known about the cosmos I would suggest you tell the friend:
The current rate of distance expansion is about 1/144% per million years.
Any largescale cosmic distance like between two distant galaxies or clusters of galaxies is increasing by about 1/144 of one percent of its size in a million years.
This expansion rate started out really big and has been steadily declining over time ever since.
That is something we can SEE by looking back into the past and it is also something the GR equation and its simplified causing the Friedman equation tell us MUST BE. It is related by the density of ordinary and dark matter. (We can see and map DM, by its optical effects. It is not a myth like DE may well be.)
It now turns out that the curve of decline, when you plot it, doesn't look like it is going all the way to zero but looks like it is leveling out at a positive percent distance expansion rate of 1/173% per million years.

That target rate is tantamount to the cosmological constant that Einstein discovered in 1917 could be (in fact had to be) added to his equation. There is room in the GR equation (our best model of how gravity works, tested meticulously for almost 100 years) for just two gravity constants: Newton's G, and Einstein's Lambda.

When you have a constant or near constant percentage growth rate then the SPEED that individual distances grow (once you specify what distance you are talking about so there is a definite speed to talk about) follow an "exponential growth curve" like money growing at 3% interest. So that is the increasing speed people talk about. It doesn't require any "push" or "energy". It is just what the equations (which tell how geometry evolves and how that evolution is affected by matter) say that geometry must behave.

Last edited: Nov 2, 2015
19. Nov 2, 2015

### marcus

I'd get familiar with this table, so when you talk to your friend and say what is increasing and what is decreasing, it means some thing definite.This from post #7, back a ways. It has some surrounding explanation.

20. Nov 2, 2015

### Daniel K

Alright. Let me try to rephrase that. (My bad I'm personally more of a verbal communicator)
The big bang somehow happened, and during the inflation period the universe started to expand at a insanely rapid rate. However after the inflation period the universe started to decelerate in expansion.
Then, dark energy (or whatever) entered the situation and the universe started to decelerate in a less rapid manner. (Example : Before it was decelerating at 100,000 kilometers per second and now it was decelerating at 50,000 kilometers per second).
In a way, this can be classified as acceleration. (This is the confusing part)
Right?