Observable Universe Size in Different Perspectives

[Arman777]

I am reading The Essential Cosmic Perspective and there says "We cannot observe light coming from anything more then 14 billion-light-years away".
( In my opinion this statement is wrong cause observable universe diameter is 46.5 billion light years. I guess authors meant something else, or Am I misunderstanding something ? )

Universe created/started 14 billion years ago so we cannot see beyond that timeline.Cause of that we have a limit of things that we can see. Now we are not in the center of the universe so my question can be awkward but an observer in 12 billion light-years away would see the same "observable universe" in size perspective or maybe also in some other perspectives ?

1-The confusing part is when we go further we go past in space so 12 billion light years away means 12 billion years ago so in that time universe was not as big as it's now.In that case the answer would be no.

2-In the other hand since "we are not in the center" according to him we are 12 billion light years away so the size of the observable universe will be the same.

I believe 2 is the correct answer.

Also every moment the radius of the observable universe increases but it does not mean anything cause in the edges of the observable universe there's nothing but CMB radiation

Thanks.

 

[Bandersnatch]

In my opinion this statement is wrong cause observable universe diameter is 46.5 billion light years.

I believe 2 is the correct answer.

You're correct on both counts. (it should be radius, not diameter, though)

Without seeing the larger context it's just a guess, but in the first case it looks like the author might not mean the radius of the observable universe, but the event horizon (distance from which light emitted NOW can no longer reach us in the future).
However, it would still be incorrect, as ~14 Glyr is the current Hubble radius (where recession equals the speed of light) and it is not the event horizon.

 

[Arman777]

You're correct on both counts. (it should be radius, not diameter, though)

Without seeing the larger context it's just a guess, but in the first case it looks like the author might not mean the radius of the observable universe, but the event horizon (distance from which light emitted NOW can no longer reach us in the future).
However, it would still be incorrect, as ~14 Glyr is the current Hubble radius (where recession equals the speed of light) and it is not the event horizon.

I see thanks for the reply ..I think they didnt want to include the expension since it may be confusing, maybe they will correct it in next chapters.

I guess there's a distinction between "entire universe" and "observable universe".
If I say something like this, "There could be a galaxy 100 billion light-year away " Is this make sense ? Since there could be another universe and within that universe another galaxy ?

 

[Bandersnatch]

If I say something like this, "There could be a galaxy 100 billion light-year away " Is this make sense ? Since there could be another universe and within that universe another galaxy ?

Sure. For all we know the universe as a whole could be infinite, with more of the same as out observable patch, any distance you like.

 

[Arman777]

Sure. For all we know the universe as a whole could be infinite, with more of the same as out observable patch, any distance you like.

I understand. .In the other hand is there chance that our universe is the only universe or current theories etc suggest that there's most likely there's other universes

 

[phinds]

I understand. .In the other hand is there chance that our universe is the only universe or current theories etc suggest that there's most likely there's other universes

There are theories that posit multiple universes but there is zero evidence for them

 

[Arman777]

I see well thanks

 

[kimbyd]

I am reading The Essential Cosmic Perspective and there says "We cannot observe light coming from anything more then 14 billion-light-years away".
( In my opinion this statement is wrong cause observable universe diameter is 46.5 billion light years. I guess authors meant something else, or Am I misunderstanding something ? )

Distance is a tricky concept in General Relativity. It is possible to accurately state that the only light we have ever observed has traveled for less than about 14 billion years, but the expansion of the universe messes with the concept of distance quite a lot. You could accurately state that that light traveled 14 billion light years, as that is the distance of the path the light traveled.

The light of the CMB, the furthest light we can observe, was emitted from matter roughly 43 million light years away. For a good fraction of the history of the universe, the light rays that were moving in our direction were getting further away. More recently, the rate of expansion slowed enough that that light started to gain ground instead, eventually reaching us nearly 14 billion years after it was emitted.

Today, the matter that emitted that radiation lies at roughly 46.5 billion light years distance. That matter has long since passed our cosmic horizon, so we won't ever be able to receive light emitted today from those galaxies.

Also every moment the radius of the observable universe increases but it does not mean anything cause in the edges of the observable universe there's nothing but CMB radiation

That's not quite why this doesn't matter. If we didn't live in a universe with dark energy, then if we could live for billions of years we would be able to see galaxies further and further away form, grow, and merge with one another.

Dark energy puts a kibosh on this, because it creates a horizon. Light that comes from galaxies that are more than something like 16 billion light years today can never reach us, no matter how long we wait. Furthermore, as the universe expands, more and more galaxies will move beyond this horizon (the horizon itself will eventually grow to about 17 billion light years and stay there). Eventually, nothing that isn't in the same galaxy cluster will remain within our horizon. So in a very real sense, our universe will, over large periods of time get smaller.

 

[Arman777]

Distance is a tricky concept in General Relativity. It is possible to accurately state that the only light we have ever observed has traveled for less than about 14 billion years, but the expansion of the universe messes with the concept of distance quite a lot. You could accurately state that that light traveled 14 billion light years, as that is the distance of the path the light traveled.

The light of the CMB, the furthest light we can observe, was emitted from matter roughly 43 million light years away. For a good fraction of the history of the universe, the light rays that were moving in our direction were getting further away. More recently, the rate of expansion slowed enough that that light started to gain ground instead, eventually reaching us nearly 14 billion years after it was emitted.

Today, the matter that emitted that radiation lies at roughly 46.5 billion light years distance. That matter has long since passed our cosmic horizon, so we won't ever be able to receive light emitted today from those galaxies.That's not quite why this doesn't matter. If we didn't live in a universe with dark energy, then if we could live for billions of years we would be able to see galaxies further and further away form, grow, and merge with one another.

Dark energy puts a kibosh on this, because it creates a horizon. Light that comes from galaxies that are more than something like 16 billion light years today can never reach us, no matter how long we wait. Furthermore, as the universe expands, more and more galaxies will move beyond this horizon (the horizon itself will eventually grow to about 17 billion light years and stay there). Eventually, nothing that isn't in the same galaxy cluster will remain within our horizon. So in a very real sense, our universe will, over large periods of time get smaller.

How can be the horizon radius 17 Billion light- year since its now 46.5 billion.Did you mean that the galaxies further then 16-17 billion light-year away galaxies will be no longer visible ?

I generally understood your idea.Since there's dark energy and galaxies move away further from us we will be not able to see them after a time.

 

[Clausen]

Distance is a tricky concept in General Relativity. It is possible to accurately state that the only light we have ever observed has traveled for less than about 14 billion years, but the expansion of the universe messes with the concept of distance quite a lot. You could accurately state that that light traveled 14 billion light years, as that is the distance of the path the light traveled.

The light of the CMB, the furthest light we can observe, was emitted from matter roughly 43 million light years away. For a good fraction of the history of the universe, the light rays that were moving in our direction were getting further away. More recently, the rate of expansion slowed enough that that light started to gain ground instead, eventually reaching us nearly 14 billion years after it was emitted.

Today, the matter that emitted that radiation lies at roughly 46.5 billion light years distance. That matter has long since passed our cosmic horizon, so we won't ever be able to receive light emitted today from those galaxies.That's not quite why this doesn't matter. If we didn't live in a universe with dark energy, then if we could live for billions of years we would be able to see galaxies further and further away form, grow, and merge with one another.

Dark energy puts a kibosh on this, because it creates a horizon. Light that comes from galaxies that are more than something like 16 billion light years today can never reach us, no matter how long we wait. Furthermore, as the universe expands, more and more galaxies will move beyond this horizon (the horizon itself will eventually grow to about 17 billion light years and stay there). Eventually, nothing that isn't in the same galaxy cluster will remain within our horizon. So in a very real sense, our universe will, over large periods of time get smaller.

Excellent post, very detailed explanation.

I do have one question about this part "More recently, the rate of expansion slowed enough that that light started to gain ground instead"
As I understand the current theory, the rapid rate of expansion of the early universe did slow down some 5 billion years ago, but we now see evidence it has sped up again due to dark energy. Is this your understanding also?

 

[kimbyd]

How can be the horizon radius 17 Billion light- year since its now 46.5 billion.Did you mean that the galaxies further then 16-17 billion light-year away galaxies will be no longer visible ?

The horizon is the distance beyond which if galaxies were to emit light in our direction today, that light could never reach us.

The matter that is today something like 46.5 billion light years away was, when it emitted the light we see, only about 43 million light years away.

 

[Bandersnatch]

I do have one question about this part "More recently, the rate of expansion slowed enough that that light started to gain ground instead"
As I understand the current theory, the rapid rate of expansion of the early universe did slow down some 5 billion years ago, but we now see evidence it has sped up again due to dark energy. Is this your understanding also?

The rate of expansion in kimbyd's post is another name for the Hubble parameter $H(t)$ - it tells you by what fraction all distances grow at a given time.
For example, its value at the current epoch $H_0$ (aka Hubble constant) netts approximately 1/144 % of growth per million years (which is just another way of writing the more familiar ~68 km/s/Mpc).
The Hubble parameter has always been and will continue to decrease, in the far future asymptotically approaching some fixed value determined by dark energy.

What used to be decelerating and has since started to accelerate is the growth of the scale factor $a$. The scale factor tells you how large all distances are compared to those same distances at some other time. It's like the nett growth, as opposed to $H$ being instantaneous percentage rate.

A good analogy to visualise the difference is a savings account in a bank. The scale factor is how much money you have. The Hubble parameter is the monthly interest rate.
If the interest rate does not change between months, the amount of savings will grow exponentially. If the rate goes down eventually reaching zero, the amount of savings will eventually stop growing. If the interest rate goes down but to some positive value*, the savings may at first grow by less every month, but eventually will start growing exponentially (i.e. there will be a change from decelerated to accelerated growth).

*Example of such a rate: 1+1/n %/month, where n is the number of months the money's been sitting on the account = the rate approaches 1 % as time passes.

 

[Clausen]

The rate of expansion in kimbyd's post is another name for the Hubble parameter $H(t)$ - it tells you by what fraction all distances grow at a given time.
For example, its value at the current epoch $H_0$ (aka Hubble constant) netts approximately 1/144 % of growth per million years (which is just another way of writing the more familiar ~68 km/s/Mpc).
The Hubble parameter has always been and will continue to decrease, in the far future asymptotically approaching some fixed value determined by dark energy.

What used to be decelerating and has since started to accelerate is the growth of the scale factor $a$. The scale factor tells you how large all distances are compared to those same distances at some other time. It's like the nett growth, as opposed to $H$ being instantaneous percentage rate.

A good analogy to visualise the difference is a savings account in a bank. The scale factor is how much money you have. The Hubble parameter is the monthly interest rate.
If the interest rate does not change between months, the amount of savings will grow exponentially. If the rate goes down eventually reaching zero, the amount of savings will eventually stop growing. If the interest rate goes down but to some positive value*, the savings may at first grow by less every month, but eventually will start growing exponentially (i.e. there will be a change from decelerated to accelerated growth).

*Example of such a rate: 1+1/n %/month, where n is the number of months the money's been sitting on the account = the rate approaches 1 % as time passes.

I'm not sure I understand this. Is the rate of expansion of the universe slowing down or speeding up, or do we know?

 

[Arman777]

The horizon is the distance beyond which if galaxies were to emit light in our direction today, that light could never reach us.

The matter that is today something like 46.5 billion light years away was, when it emitted the light we see, only about 43 million light years away.

I see that's kind of amazing

 

[phinds]

I'm not sure I understand this. Is the rate of expansion of the universe slowing down or speeding up, or do we know?

The expansion is accelerating.

 

[Bandersnatch]

But the rate of expansion is slowing down.

 

[phinds]

But the rate of expansion is slowing down.

I thought the rate of ACCELERATION was slowing down, meaning the rate of expansion is continuing to increase and will continue to continue to increase.

 

[Bandersnatch]

I thought the rate of ACCELERATION was slowing down, meaning the rate of expansion is continuing to increase and will continue to continue to increase.

I'm not sure what would that mean, but it's likely a matter of using different names for the same thing.

Here's the standard usage:

$a(t)$ - scale factor, 'size of the universe' as compared to today (not the observable universe - the distance between any two arbitrarily chosen points in the universe, e.g. some two galaxies)
$\dot a > 0$ - size of the universe is getting bigger over time, 'expansion of the universe'
$\dot a < 0$ - size of the universe is getting smaller over time, 'contraction of the universe'

$\frac{\dot a}{a} = H$ - Hubble parameter, 'rate of expansion' = by what fraction of its size does the universe grow per unit time
$\dot H > 0$ - rate of expansion is increasing over time, 'accelerated rate of expansion'
$\dot H < 0$ - rate of expansion is decreasing over time, 'decelerated rate of expansion'

$\ddot a > 0$ - growth of the universe is speeding up over time, 'accelerated expansion'
$\ddot a < 0$ - growth of the universe is slowing down over time, 'decelerated expansion'

Expansion, decelerated/accelerated expansion:

Rate of expansion:

 

[Bandersnatch]

I'm not sure I understand this. Is the rate of expansion of the universe slowing down or speeding up, or do we know?

Can you tell me where have I lost you with the interest rate analogy? Can you see how you can gain more money in interest (expansion accelerating) even though the interest (expansion) rate is going down?

 

[phinds]

Can you tell me where have I lost you with the interest rate analogy? Can you see how you can gain more money in interest (expansion accelerating) even though the interest (expansion) rate is going down?

It's terminology. We're saying the same thing in terms of what's happening. I look at the interest as the rate of acceleration and the overall amount of money as the expansion, so I see the acceleration (interest) going down slightly but the amount of money (expansion) continuing to increase more and more because of compound interest.

 

[Bandersnatch]

That particular question was aimed at Clausen. But since you answered:

I look at the interest as the rate of acceleration

Standard usage (given in post #18) notwithstanding, you've called Hubble parameter (interest rate) 'rate of acceleration'.
In what sense would it be justifiable to call it that, considering that it remained positive and monotonically decreasing throughout both the deceleration and acceleration phases of the expansion?

overall amount of money as the expansion

If the overall amount is X and stays X, then where's the expansion? It has to be a time derivative. I.e. expansion is when overall amount grows.

We're saying the same thing in terms of what's happening.

Yes, I do believe so. I hope you don't mind me nagging you like that - if I sound nitpicky it's just because I think it's important to be precise and avoid introducing unnecessary confusion wherever possible.
Since generally growth/reduction over time implies first time derivative, and acceleration/deceleration implies second time derivative, one should make sure this meaning is reflected in use.

 

[phinds]

That particular question was aimed at Clausen. But since you answered:

Standard usage (given in post #18) notwithstanding, you've called Hubble parameter (interest rate) 'rate of acceleration'.
In what sense would it be justifiable to call it that, considering that it remained positive and monotonically decreasing throughout both the deceleration and acceleration phases of the expansion?If the overall amount is X and stays X, then where's the expansion? It has to be a time derivative. I.e. expansion is when overall amount grows.Yes, I do believe so. I hope you don't mind me nagging you like that - if I sound nitpicky it's just because I think it's important to be precise and avoid introducing unnecessary confusion wherever possible.
Since generally growth/reduction over time implies first time derivative, and acceleration/deceleration implies second time derivative, one should make sure this meaning is reflected in use.

I agree. My terminology may be sloppy. At the end of the day, what matters is that the distance is accelerating (without proper motion) and is going to continue accelerating even if it is doing so at slightly lower rates of acceleration over time.

 

[Chronos]

For distant observers the current age of the universe is exactly the same right now as it is here - just like you are exactly the same age at present no matter where you happen to be. The question of what the universe looked like to a remote observer [say 12 billion years in our past] is equally obvious. That universe was only 2 billion years old back then, therefore the most ancient light visible to them at that time was no more than 2 billion years old. Due to expansion, the current distance of remote emission sources in the universe is a tricky issue. Suffice it to say, the distance traveled by photons emitted at great distances exceeds what existed at the moment of their emission

 

[kimbyd]

I'm not sure I understand this. Is the rate of expansion of the universe slowing down or speeding up, or do we know?

The rate of expansion is defined as recession velocity over distance. An object that is twice as far away as another object will be receding at about twice the speed.

If the rate of expansion is a constant, then as an object gets further away, its recession velocity will increase.

This is why I prefer to use the term "accelerated expansion", rather than to say the expansion is accelerating. In a universe with an accelerated expansion, objects within the universe are getting further away from one another at an accelerated rate. The rate of expansion (recession velocity per unit distance) will still be either decreasing or constant (there are good reasons to believe it can't increase).

 

[stefanbanev]

...

Now we are not in the center of the universe so my question can be awkward but an observer in 12 billion light-years away would see the same "observable universe" in size perspective or maybe also in some other perspectives ?

1-The confusing part is when we go further we go past in space so 12 billion light years away means 12 billion years ago so in that time universe was not as big as it's now.In that case the answer would be no.

2-In the other hand since "we are not in the center" according to him we are 12 billion light years away so the size of the observable universe will be the same.

> Now we are not in the center of the universe so my question can be awkward but an observer in
>12 billion light-years away would see the same "observable universe" in size perspective or maybe
>also in some other perspectives ?
>1-The confusing part is when we go further we go past in space so 12 billion light years away means
>12 billion years ago so in that time universe was not as big as it's now.In that case the answer would be no.

The observer 12 billion light-years away (the observer whom you may observe (in principle)) would witness universe 2 billion years old. If he for some reason is broadcasting what he sees (regarding size of universe he sees) in his message you may read that he sees 2bln years old universe.

>2-In the other hand since "we are not in the center" according to him we are 12 billion light years away so
> the size of the observable universe will be the same.

The observer 12 billion light-years away (the observer whom you may observe (in principle)) would witness universe 2 billion years old so, for him there is nothing farther then 2 bln light years away; thus, those observer has no an option to observe you so, from perspective of those observer - you do not exist (in his broadcasting you can not find in principle any evidences of your existence).

 

[rootone]

Now we are not in the center of the universe ...

We never were.

 

[phinds]

We never were.

Shows how useful commas can be.

 

[Paul Kent]

Science Advisor,
Thank you for the plots. Visuals always appreciated in a physics discussion.
Feedback:
If the universe is expanding a constant rate, as can be seen from nearly the entire history of the expansion, then the expansion is not slowing down. If you viewed a galaxy moving away from you at say 6 Gy and then again at 10 Gy it would be receding from you at the same rate. A galaxy twice as far away would still be receding at twice that velocity. This would also be true of the event horizon. A better way to understand this is to consider the perimeter of the circle. The observable universe exists along that perimeter. The perimeter of the circle scales linearly with the radius. The co-moving coordinates describe the expansion in this manner.

 

[PeterDonis]

If the universe is expanding a constant rate, as can be seen from nearly the entire history of the expansion

No, that's not what is seen from the entire history of the expansion. The entire history of the expansion shows change in the rate of expansion--it was decelerating in the early universe, then a few billion years ago it started accelerating.

 

[stefanbanev]

We never were.

A wrong quote

We never were.

>"Now we are not in the center of the universe ..."
- that was the quote from the original post not (not mine).

Actually, I'm in the center of universe; any other observer may make the same claim...

 

[rootone]

- that was the quote from the original post not (not mine).

Actually, I'm in the center of universe; any other observer may make the same claim...

Ooops sorry, don't know how I did that.
but yes everyone is at the center of what is observable for them.
The whole Universe may or may not be infinite, and need not have a center anywhere,
just as there is no place on the surface of a sphere which could be called a center.

 

[Arman777]

We don't even know the universe is sphere. I don't think there's any meaning calling "center of the universe", in this sense its just meaningless

 

[phinds]

Actually, I'm in the center of universe; any other observer may make the same claim...

Absolutely false. You are in the center of the Observable Universe, NOT "the universe"

EDIT: OOPS ... I see rootone beat me to it.

 

[phinds]

We don't even know the universe is sphere.

Actually, we know that is is NOT a sphere. If it were, it would have a center and it does not.

 

[stefanbanev]

Absolutely false. You are in the center of the Observable Universe, NOT "the universe"
...

Well, it is not false; in fact, the existence of "the universe" if it is not an observable one (in broad information sense) is matter of fate and believe...