# Age versus Size of the Universe

1. Feb 8, 2013

### Johninch

I have learned a lot about cosmology on this forum, but I’m still behind on the logic.

So far I have understood that, since the universe is everything, it cannot have a center nor a boundary. But it does have an expansion and that’s when my problems start.

I would like to concentrate on a couple of questions, in order to make some progress:

- if we know the age of the universe and we know its rate of expansion, why is there so much discussion about its total size?
- if the size of the universe is finite, how can the universe be isotropic?
- assuming that the universe is flat and finite, how can it not have a boundary?

I am not talking about the observable universe, I am talking about the total universe. Further, I am assuming that BBT refers to the total universe.

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2. Feb 8, 2013

### Johninch

Thanks, it's a good revision, but it doesn't answer my questions.

It does however mention that the consensus is that the universe is nearly flat and therefore extremely large, although not infinite.

I would have quite a problem with BBT if it were suggested that the universe is infinitely large, but even if we just stick with the assumption that it is extremely large, this emphasizes one of my problems.

If we increase our estimate of the size of the universe to near infinite proportions and we have a fixed idea of the rate of expansion (including variations over time so far), what happens to our estimate of the age of the universe? Does that approach infinity too?

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Last edited by a moderator: Feb 9, 2013
3. Feb 8, 2013

### phinds

Does the surface of the earth have an edge?

The universe can be finite but unbounded, like the surface of the Earth.

4. Feb 8, 2013

### marcus

I see Phinds beat me to it
Second question: For the 2D creatures living on the surface of a sphere, the sphere surface (their space) is isotropic.

Third question: Think of a "Pac Man" flat 2D universe which is a square with opposite edges identified. So if a feature slides off the right edge he reappears coming in on left. Likewise top and bottom. Topologically it is a torus, the 2D surface of a donut. But there is no curvature. This universe is not embedded in any higher dimensional space. It is an edgeless flat square which has been made edgeless by identifying or "gluing" opposite sides.

These 2D sketches have 3D analogs which are not too hard to imagine living in. Don't try to picture them from the "outside" because there is no outside where you could stand and look at them. The way to conceptualize is to imagine the experience of living in such a space and moving around in it. Stretching string, light rays, circumnavigating etc.

First question: We know the expansion rate as a PERCENTAGE PER UNIT TIME and we can estimate the past history of this percentage rate.
That does not tell us the overall absolute size.
You are very welcome to ask more questions about this. If it isn't clear why knowing percentage expansion rate history does not tell absolute size, keep on asking. I don't want to make this post longer because it may not be necessary.

The present Hubble constant is equivalent to saying that distances increase by 1/139 of one percent every million years. It tells us what individual distances do. It does not tell the overall absolute size.

The classic model does not include a model of the universe at the precise start of expansion so there is no "size" to start with. Some newer models (like Loop quantum cosmology) DO include the start of expansion and may have a finite size (at for example the time of the bounce---there is a bounce instead of a mathematical failure). But so far the overall size at start of expansion has not been determined in the new, singularity-free models. So we only know percentage growth and we cannot pinpoint initial size.

However it might eventually turn out to be possible to estimate PRESENT size and then extrapolate back.

5. Feb 8, 2013

### phinds

Yes, but as always, you present a MUCH more complete and coherent discussion.

6. Feb 8, 2013

### Johninch

Marcus beat me too, while I was composing this answer to Phinds. I will study Marcus' reply afterwards.
No, the surface of the earth does not have an edge and the universe is also not like the two dimensional surface of the earth, so it's irrelevant.

Are you saying that the universe is closed? If so, the universe has the shape of a sphere and will have a boundary. Otherwise, what does closed mean?

The consensus is that the universe is flat or nearly flat. If it's flat, it will not have an edge or boundary, but the problem for me is that it would be infinitely large, according to the generally accepted model of a flat universe.

If it's nearly flat, it will be huge and presumably this is the reason for the discussion about it's size, because nobody can say how huge it is. My question is, if we debate the size of the universe, do we have to adjust the age of the universe in order to get to the speculated size, or do we have to adjust the rate of expansion, or what?

I would also like to know, what do the inhabitants of the oldest galaxy see. Does the universe look isotropic from there? This relates to the boundary question.

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7. Feb 8, 2013

### Johninch

My further questions about boundary are contained in my posting to Phinds.

Concerning size and age: I can see the problem of not having the starting size, but we do have the diameter of the observable universe (93 mly) and the current rate of expansion (70 km/sec/Mps) and estimates of the lower rates of expansion in the past. So logically we should be able to extrapolate back to a smaller size near to the BB.

Then we have various data from WMAP etc, plus other observations from astronomy, so altogether we can come up with a history of the universe including BBT. Ok, that's all we can do in the observable universe.

What we don't have, are reliable estimates about the size of the unobservable universe. I have seen some extremely big figures, which would tie into the concept of a nearly flat universe. What bothers me is, having done our observations and calculations for BBT, how do we square our age of the universe and expansion rates with the size of the total universe.

The unobservable universe also came from the BB didn't it? I mean, the larger the universe, the older or faster expanding it is. So just how reliable is the figure of 13.7 bn?

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8. Feb 8, 2013

### phinds

THIS is that statement that lead me to attempt to help you understand that it is NOT necessary that if something is finite it has a boundary. The surface of the earth is finite and yet does not have a boundary. Do you dispute this? By analogy the total universe also can be finite and yet unbounded.

The univerese is NOT, as far as we know, shaped like a sphere, but WHATEVER the shape, it does not have to be bounded (or unbounded for that matter --- it has to be one or the other but we don't know which).

9. Feb 8, 2013

### Naty1

We don't. Nobody knows the size of the universe. On the surface of the earth, you might be able to make a guess about the total size of the earth based on the horizon distance, curvature, etc. But for the universe you can't even make such an estimate based on any existing observations or theory.

Maybe a crude analogy would be trying to figure out how far a distant object is from you on earth a foggy day, dead of night [no light signals whatsoever, no radar reflection,etc] while it's drifting away.....you can't see it nor detect it in any way. The cosmological 'fog' is the origin of relic radiation, called the surface of last scattering.

For calculations on what we do know, see Marcus' discussion here:

New satellite based observations now suggest it is about 13.4 by old.
In future years we'll probably have newer observational data.

10. Feb 8, 2013

### Johninch

I already replied that I agree, the surface of the earth does not have a boundary. So what? We are living in 3d space, so your analogy is meaningless.

I already told you that the universe is not shaped like a sphere. It's flat or nearly flat.

What is the basis for your statement that it does not have to be bounded? You say it has to be one or the other but we don't know which. You seem to be suggesting that I am wrong to assume a boundary. Why? I am only saying that finite things usually have a boundary, so the universe may have one too. What's wrong with that?

I am aware that everybody assumes that the universe has no boundary, but the whole point of my questions is to understand the logic of these matters.

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11. Feb 8, 2013

### Whovian

The analogy can be extended to a 3-dimensional "surface."

Nearly flat doesn't mean "not shaped like a sphere," and there are plenty of other models, such as a 3-torus-like Universe. The 3-sphere is an example.

What happens when you cross that boundary? It should be theoretically possible, and once you do, you're ... umm ... outside the Universe. And the Universe, by definition, is everything, and thus being outside the Universe is impossible. (Again, by definition.)

12. Feb 8, 2013

### marcus

Whovian and Phinds, great answers! I hope the questioner's curiosity is eventually satisfied.
It's important for people to realize that what is meant by "nearly flat" could in fact be "3-spherical but very large". A very large spherical surface would seem nearly flat to creatures living in it. Near flatness, in that case, just translates into the 3-sphere having a very large radius of curvature.

And a nice thing is that the radius of curvature can be estimated from today's observational data. Alternatively, bounds on the CIRCUMFERENCE of the 3-sphere can be estimated. That is just 2 pi times the radius of curvature. It is how long you would have to travel in a straight line before you get back to your point of departure.

The calculation, in case some readers haven't seen it before, is very simple. You take the Hubble distance (often given as 13.9 billion ly, or 14 billion for round numbers) and multiply by 2 pi. That gives around 88 billion ly. Then you divide that by the square root of minus the Ωk number that is derived from all the combined data from CMB observations, supernovae, galaxy counts etc.

the estimate of Ωk keeps getting better as more data is collected. A good recent source is Hinshaw et al, which was just revised as of 30 January. Just google "Hinshaw nine-year"
These are the final results of the 9 year WMAP project. The report is called "WMAP9" for short.
For instance look at their Table 10, on page 20, where they give 95% confidence intervals which depend on which data sets they combined to get the result.
Combining all the data sets (WMAP+eCMB+BAO+H0 +SNe) gives the results in the rightmost column.
The confidence interval for - Ωk is [0.0025, 0.0105]

Let's take the smallest thing to divide 88 billion ly by, that will give the largest circumference. The square root of 0.0025 is 0.05. So divide 88/0.05 = 1760 billion ly.

This works as long as the estimate of Ωk is negative, so when you take minus you get a positive number, and the square root makes sense.

So according to that confidence interval, from Table 10, the largest the circumference could be is 1760 billion ly.
Now what is the SMALLEST it could be? Well the square root of 0.0105 is about 0.1 and dividing by that is like multiplying by 10, so the smallest the circumference could be is around 880 billion ly.

The main thing is we have no evidence for there being "space outside of space" or for there being any boundary to space. So it could be infinite, or it could be something like a 3-sphere. These are the simplest things to imagine and the model builders are normally aiming for the simplest model with the best fit to the data.
Googling "Hinshaw nine-year" gets you http://arxiv.org/abs/1212.5226
the dataset abbreviations are explained on page 2.
eCMB means "external CMB dataset" from other than WMAP itself, i.e. South Pole Telescope (SPT) and Atacama Cosmology Telescope (ACT). Of course SNe means supernovae data. BAO (baryon acoustic oscillation) basically means counting galaxies at different distances to detect "ripples" in the average bulk matter of the universe.

Last edited: Feb 8, 2013
13. Feb 8, 2013

### Johninch

No, I think it is not theoretically possible. If the universe is everything, you can't go outside it. If the universe is expanding at greater than the speed of light in the outer regions, so would be the boundary.

The boundary would be where an observer could (perhaps) see galaxies on one side of the sky but definitely not on the other side because there are none. Can you give me a reason why this is not possible?

I am not making up stories, I am just trying to make sure that it is illogical to think of a boundary.

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14. Feb 8, 2013

### Chronos

The observable universe definitely has a 'boundary' of sorts. It is called the particle horizon, which, simply put, is merely the age of the universe multiplied by the speed of light. We do, however, have solid reasons to believe the entirety of the universe is far larger than the little patch within our particle horizon. It could even be infinite, although the only thing we can deduce with any degree of reliability is a minimum size. It is worth noting that the particle horizon is not a boundary in any conventional sense. Objects in the universe may freely pass beyond our particle horizon without 'leaving' the universe. They merely become unobservable. Every observer in the universe is 'special' in this sense, they all have their very own personal particle horizon that is unique to their location.

15. Feb 8, 2013

### marcus

You understand do you not, that space can expand without haveing any other space outside it to expand into.

The universe is usually considered to be all space and the space is what is expanding so you are not imagining a boundary of the universe, but a boundary to the part occupied by matter. I see nothing wrong with imagining that. Why not?

But it makes things mathematically very complicated and there is no evidence that matter is like that: confined to some limited part of the universe.

The simplest mathematical picture is that however much space there is, it is uniformly filled with matter---over large scale average density is approximately even.
There is no evidence this is NOT true so there is no reason to unnecessarily complicate things by imagine matter in only one part of the universe.

They are always going for the simplest best-fit model. The simplest that gives the best fit.

Of course cosmologists are always looking for evidence that would challenge their consensus model. One of the things they are always sounding the alarm about is someone thinks he has seen some evidence of largescale NON-uniformity. Statistically fewer galaxies in some direction, or something. So far I've seen a bunch and they always turned out to be "false alarms" and were eventually ignored or abandoned.

Some inflation scenarios give rise to bubbles in the midst of a vast irregular universe in which expansion is occurring at different rates, so that would represent a kind of non-uniformity. But one does not actually USE such models to fit observational data to. They are more in the realm of speculation
================
One reason large scale uniformity is the simplest assumption is that in GR, which is the well tested prevailing law both of gravity and geometry, matter and geometry interact on an intimate basis. They shape and guide each other. It is natural to think of matter and geometry as co-extensive. Would make the math a lot harder to have matter confined to only one part of an expanding universe. And after all, why should it be?

Last edited: Feb 8, 2013
16. Feb 9, 2013

### Johninch

I consider that the universe is everything which exists. The universe includes all baryonic matter, dark matter, dark energy, dirac space and anti-matter. There is nothing beyond the universe because nothing does not exist.

I have no problem with the assumption that matter is uniformly distributed within the observable universe. If we assume that the total universe is several orders of magnitude larger than this, then a locally uniform distribution of matter would seem to be a reasonably likely local phenomenon. However, it seems speculative to assume that this local density and uniformity is repeated over the whole universe.

I interpret your remarks concerning the irregularities in the CMBR as meaning that although we interpret those irregularities to result in the formation of matter and galaxies, we nevertheless assume that the expansion of the universe has always proceeded at an equal rate for all galaxies everywhere. This would give us the even distribution. Please check: I previously understood that some galaxies are receding much faster than others, which would give the universe a non-uniform distribution and a non-spherical shape. But now I understand that the difference in the calculated speed of distant galaxies is only (mainly) due to distance and time, right?

You apparently misinterpreted my post concerning the boundary. I was referring to the boundary of the universe and not the boundary of the part occupied by matter, baryonic or otherwise. That is to say, outside my imagined boundary there is not anything. The imagined situation is the following:

I am magically and immediately transferred from here to a planet on the edge of a galaxy where I can only see the local milky way plus other galaxies on one side of the sky only. All of those galaxies appear to be receding at a very fast and accelerating rate. On the other side of the sky I do not see anything at all. It is totally dark to my eyes and to all of my very advanced instruments. I fully understand BBT. What do I conclude?

-My planet is on that boundary of the galaxy farthest from the rest of the universe.
-My galaxy is at a boundary of the universe, beyond which there is no more universe.
-As I do not observe anything in the “dark” direction, I have to assume that there is absolutely nothing there.
-To make sure, I send a rocket up. It performs “normally” but the onboard instruments do not detect anything (except itself).

What’s wrong with that? Is there a reason why the imagined planet cannot logically exist?

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17. Feb 9, 2013

### Johninch

Thanks for your clear summary Chronos. The only piece which I object to is the reference to infinity.
I don't want to start a philosophical discussion, I only want you to know that I noticed it!

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18. Feb 9, 2013

### Naty1

Marcus:
I am not so sure as Marcus about the last sentence....the 'speculative' part.... I note that each day we receive new cosmic background radiation,CMBR, from which at the time of its origin the early seeds of the universe were present, and those signals appear with the same characteristics as yesterday's, and the day before and the day before that and.....so forth. So from what Marcus has taught me I conclude as the observable universe grows each day, it exhibits the same radiation characteristics as the prior day and that at least suggests that there is nothing unusual just beyond yesterday's observations. So I expect tomorrows CMBR
will be just like todays.

Chronos:
Another way to express this, I think, is that an infinite universe cannot so far be ruled out.

19. Feb 9, 2013

### timmdeeg

Let's assume that the universe is exactly flat and obeys the FRW model. Flat then means locally flat because nothing else we are able to measure. However the model says that an arbitrary oberver will agree to that regarding his local position in the universe. Thus globally viewed the curvature is constant, well in accordance with the cosmological principle one of the consequences of which is that there is no center and no boundary.

Still, even being exactly flat leaves the global structure of the universe, it's topology, open. In case the universe has a compact topology, e.g. a 3-torus which is flat locally, then it's size is finite. Some date indicate this possibility.

If it's nearly flat, we know less.

20. Feb 9, 2013

### marcus

Hi John, I'm more of a cosmology-watcher than a participant. I follow developments as best I can, and love the subject. This is my personal perspective. To answer the part I highlighted in blue I would say that cosmology is a mathematical science i.e. it aims at the simplest best-fit mathematical model. And GR is our law of gravity and our law of geometry (why triangles add up to approximately but not exactly 180 and how matter affects this) that we base the cosmic model on.

Someday GR will be improved but for now it is the accepted dynamics of geometry that has been tested repeatedly in many ways and passed all the tests and has proven remarkably accurate.

So the key thing to realize is that cosmology is an APPLICATION of the accepted law of gravity/geometry. The aim is not merely an ad hoc model that fits the observational data- it is to find the simplest bestfit model which is a solution of the GR equation.
The simplest best-fit model which accords with the currently accepted dynamics of geometry and matter.
I suppose that LOGICALLY you can send a rocket probe into non-existence and you can imagine a region of nothingness and a region of existence and a boundary between them. I can't think of a LOGICAL reason not to imagine a rocket going thru the boundary and its onboard sensors not detecting anything except its own existence.

But I don't think that one can MODEL that situation with a SOLUTION OF THE GR equation. A region of non-existence is not a feature of our currently accepted dynamics of geometry and matter, which we are pretty much stuck on using as the best available so far.

Now to respond to the blue highlight paragraph. I think the assumption of approximate uniformity is a reasonable working assumption because
1) it is simple
2) so far no evidence to the contrary has withstood scrutiny

People regularly review this assumption to see how it is holding up, and people challenge it now and then. It is a serviceable working assumption, I would not think of it as an article of faith. As long as the model continues to fit the data people will keep on using it---until something better shows up.

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21. Feb 9, 2013

### marcus

Hi Naty, in post #18 it sounded as if you were quoting me but I think you were actually quoting John, so i was a bit confused and didn't see how to respond.

22. Feb 9, 2013

### Johninch

However, in the part of your reply quoted above, you are being too generous towards my logic!

My thought experiment of sending a rocket in the opposite direction to all of the known universe does not involve going through a boundary into nothingness. That's impossible. The rocket is part of the universe and is enlarging it.

This is my way of illustrating how the universe could have a boundary. The universe does not need any space to expand into, it creates its own space by expanding. This is what you told me already, so I am sure you agree.

With my thought experiment I am merely wanting to show that it's possible to be at the boundary of the universe without implying that there is anything beyond. So far I have read everywhere that the universe does not have a boundary. So if my experiment is possible, then it can have a boundary.

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23. Feb 10, 2013

### Naty1

Marcus:
from #18:

DUDE!! I was throwing you a COMPLIMENT..... from several years of prior discussions.
Relax and enjoy; Bask in the glory!! [LOL]

24. Feb 10, 2013

### marcus

Thanks for the compliment, Naty! What puzzled me in your post #18 was that it looked like you were quoting me, saying "it seems speculative" when the words in quotes were actually from somebody else. I knew I had not said what you had me down as saying, so I went back looking for those words and found they were from Johninch.
You give a cogent reason for not regarding the cosmological assumption of uniformity as all that speculative. I guess now that I think of it the only problem was your post should have begun:
=======
Johninch:

......

I am not so sure as Johninch about the last sentence...
=======

What you were saying made a lot of sense, you just had the people's names confused. I see now how I should have responded.

25. Feb 10, 2013

### marcus

I wouldn't call the cosmological principle (the basic uniformity assumption) speculation, exactly. It think it comes under the heading of Occam's Razor---the idea is that in a mathematical science you should use the SIMPLEST model that fits.

You keep the model simple until you actually get evidence that you need to make it more complicated. And you keep watching out for such evidence!

I would call it speculative to start imagining some boundary off somewhere too far away for us to see, when we have no indication of a boundary. Some day we might, but we haven't yet seen any suggestion of one that withstood scrutiny.

I would likewise call it speculative to start assuming there is a center of the universe far away in some direction (but we just don't know in what direction to point in :-)

Those would be unnecessary complications for which there is no justification. But we should always keep an eye out for any asymmetries in the statistics that might suggest NON-uniformity. And people do watch for that, and periodically sound the alert. What I've seen happen is that the alleged evidence is carefully examined---and so far has been found wanting, and dismissed.

Last edited: Feb 10, 2013