Question reguarding the expanding universe

[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.

 

[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.

 

[Chalnoth]

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

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.

 

[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?

 

[Daniel K]

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

 

[Daniel K]

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

 

[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"

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 - H_∞² = [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 into 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.)

 

[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.

 

[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)

 

[Chalnoth]

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

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.

 

[marcus]

...however, this growth of the Hubble radius should be decelerating.

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

 

[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.

 

[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."

 

[marcus]

...
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.
.

Right!

...

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."

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.

 

[Daniel K]

THANK YOU SO MUCH I FINALLY UNDERSTAND IT

 

[marcus]

My pleasure! Thanks for the persistent/thoughtful questioning.

 

[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?

 

[marcus]

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)
...

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.

 

[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.

Here's a history of the H(t), expressed as a percentage distance growth rate"

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

 

[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?

 

[Daniel K]

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.

That makes sense. Sorry I didn't see that before.

 

[marcus]

No problemo, for Pete's sake. You are holding up your end in the discussion really well.

If you want to show how the decline in H(t) slows down, that table could help
Here's a history of the H(t), expressed as a percentage distance growth rate"

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

From 11 billion to 12 billion the denominator increased by 7 (from 128 to 135) that is one way that shows a fraction getting smaller, increasing the denominator.
From year 12 billion to 13 billion the denominator increased by 5---not as much.
From 13 to 14 billion, again by 5.
But from 14 billion to 15 billion it only increased by 4!

I wouldn't use the words acceleration and deceleration to describe this at all. H(t) is all important, it runs the show and it is what the Friedman equation is ABOUT, but it is not a speed.

The important thing about H(t) is that as time goes on it is stabilizing as a constant percentage growth rate
AND GROWTH AT A CONSTANT PERCENTAGE RATE IS EXPONENTIAL. Understand exponential growth. And if you pick some sample distance to watch grow, the growth can be expressed as a speed. And that speed can increase. In fact in exponential growth with constant (or near constant slowly declining percentage rate) the speed DOES increase.

That's all the hype and screaming about "acceleration" and "dark energy" is about---it is a way of telling you that distance growth curves are evolving towards exponential growth shape, with a longterm constant percentage.
It's a way of telling you that which appeals to the journalists and the lay public, who like to hear about "energy" and are thrilled by putting the pedal to the metal and "accelerating".

Before year 7 billion or so, the H percentage growth rate was dropping so fast that you didn't get exponential growth. Like the bank paying you 3% on savings the first year and then 1% the next, and then 1/4% the next.

Contrast that with a steady or nearly steady rate.

The first year you have 1.03
The next year you have (1.03)(1.03) times your original money.
The next year you have (1.03)(1.03)(1.03)...
Each year your dollar gain is more.
That translates into increasing speed when we talk about distances instead of dollars.

As long as the interest rate is steady, or declining but not too fast, you have a basic exponential growth shape.

So it is the APPROACH TO CONSTANCY of H(t) percent RATE that translates into "acceleration" of whatever distance you choose to track's growth speed.

 

[Daniel K]

Alright, thanks so much for all your intricate answers.
Off topic question: are you a professor?
You appear to be informed on many subjects and you're very good at teaching it.

 

[marcus]

retired did do some teaching at college level, though, which was fun!
As I said earlier, I appreciate your persistent and thoughtful questioning.
The idea, with a quantitative science, is to get a quantitative feel or intuition for it. How the different quantities are related. Which influences which.
I don't really know but it could be a chance for you to extend the way you think in some new directions.

 

[marcus]

Here's a thought. Earlier you mentioned your interest in the Hubble sphere. You might be interested in a fact about the size of the Hubble radius

Hi.
I was recently researching the Hubble Sphere - a concept that is within cosmology - and someone claimed something interesting.
...

You can read off the size of the radius of the Hubble sphere, in billions of lightyears, from the denominators of the percentages in the earlier table
Here's a history of the Hubble radius R(t)

year        Hubble radius in billions of lightyears
1 billion        1.5
...
...
11 billion      12.8
12 billion      13.5
13 billion      14.0
14 billion      14.5
15 billion      14.9
...
...
50 billion      17.3  (approx. equal to R∞ the longterm size of radius)

Our present-day Hubble radius in this year 13.8 billion is 14.4 billion LY
You have to remember to put in the decimal point.

 

[Phyics111]

Sorry to revive a dead discussion, although I was just reading through this and I have a question.

Couldn't the increasing rate of expansion, as explained by Marcus, be explained due to the weakening of gravity?
As time continues, the universe expands and the matter and therefore mass is spread out. This dispersal of mass has the effect of making gravity weaker, and so the deceleration of space would begin to weaken. This would be observed by us as acceleration.

 

[Jorrie]

Sorry to revive a dead discussion, although I was just reading through this and I have a question.

Couldn't the increasing rate of expansion, as explained by Marcus, be explained due to the weakening of gravity?
As time continues, the universe expands and the matter and therefore mass is spread out. This dispersal of mass has the effect of making gravity weaker, and so the deceleration of space would begin to weaken. This would be observed by us as acceleration.

No, without any form of dark energy, the expansion and recession curves would have looked like this:

Compare this to the presently accepted curves given in the other thread: https://www.physicsforums.com/threads/dark-energy-question.847947/#post-5317959

 

[cosmos1111]

Before year 7 billion or so, the H percentage growth rate was dropping so fast that you didn't get exponential growth. Like the bank paying you 3% on savings the first year and then 1% the next, and then 1/4% the next.

This doesn't make sense to me.
Although for some close objects there wouldn't be exponential growth, it seems that exceedingly distant objects would experience it.

The H percentage growth could drop arbitrarily fast, however you could just point to another point in space that is so distant that it still experiences the experiential growth.

 

[Jorrie]

This doesn't make sense to me.
Although for some close objects there wouldn't be exponential growth, it seems that exceedingly distant objects would experience it.

The H percentage growth could drop arbitrarily fast, however you could just point to another point in space that is so distant that it still experiences the experiential growth.

A % growth means it is the same for all distances, near and far. With 'near' I mean at least far enough so the the expansion is isotropic. Just like 1% interest is 1%, irrespective of the amount you invested.

True "exponential growth" happens when the % growth is constant. This only occurs when the matter and radiation densities become negligible.

 

[cosmos1111]

Ahhh, that was my mistake.
I was under the impression that exponential growth meant the distance and speed correlation between galaxies.
Thanks for clearing it up.

Also, I have a follow up question real quick.

So it is the APPROACH TO CONSTANCY of H(t) percent RATE that translates into "acceleration" of whatever distance you choose to track's growth speed.

Once the universe is at a constant percentage rate growth, will everything continue to accelerate forever?

 

[Chalnoth]

Once the universe is at a constant percentage rate growth, will everything continue to accelerate forever?

As far as we know, yes. Until there is nothing left in the universe. See here for a good description of the far future to the best of our understanding:
https://en.wikipedia.org/wiki/Future_of_an_expanding_universe

 

[marcus]

Once the universe is at a constant percentage rate growth, will everything continue to accelerate forever?

Yes.
If the growth rate H = a'/a really does level out at a constant then each year a distance will increase by a bit more than it increased last year.

Just like if the bank pays a constant interest rate of, say, 1%, your savings will increase by a bit more than they did the previous year.

 

[Martin0001]

As per so called "cosmological constant", lambda, Einstein himself called it "his biggest blunder".
Now it apears that lambda is real after all.
More interesting thing is that lambda may not be a constant at all, only may grow with progress of time.
This could lead to an interesting end of the world scenario, still two dozens of billions years away at least, where everything disentangles and all components (galaxies, then stellar systems, then stars and planets, then chemical molecules, then atoms, then hadrons, then any gravitational singularities (if exist)) would disentangle and any basic components left (photons, leptons, quarks) would inflate away from each other to infinity, to form some bizarre singularity like phenomenon named Big Rip.
Essentially you would end up with situation where each basic building block of matter is surrounded by a separate, "personal" event horizon, so no interaction would be possible.
In such scenario entropy in any point of space would reach maximum possible value, hence time would end.
Last year some evidence indicating possibility of such an outcome was published.

 

[PeterDonis]

Last year some evidence indicating possibility of such an outcome was published.

Reference, please?

 

[Martin0001]

Reference, please?

http://journals.aps.org/prd/abstract/10.1103/PhysRevD.91.043532#nf