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Cosmos now Bigger!

Posted October 14, 2010 4:00 AM by Jorrie
Pathfinder Tags: Size of the universe WMAP7

With WMAP now decommissioned and 'parked' in a solar orbit, the data analysis is going ahead for at least another two years (it should be the 9-year data set by then). The 7-year data set has just been released and although there are no very significant changes to the 5-year data1, I've spotted a quite subtle one. With the better accuracy now available on many (slightly revised) parameters, the minimum size of the total universe has doubled.

As I've shown in this 2008 Blog entry, the minimum diameter of the total universe was 800 Gly (billion light-years) at that time. Now it appears to have at least doubled, meaning the minimum volume has increased at least 8-fold. Not because of cosmic expansion, just due to tighter data tolerances.

Here's how it works. Out of the WMAP data comes the total density parameter2: Ω = 1 ± 0.03. Precisely one means a spatially flat (and potentially infinite) total universe. When smaller than 1, it means an open (also potentially infinite) total universe. However, when larger than 1, it indicates a spatially closed, finite universe, unbounded, but with no boundaries (like the surface of a sphere). The circumference of such a sphere represents the diameter of the 3-D universe, i.e., how far you have to travel to be in the same location that you have started from.

For Ω > 1, one can calculate the present radius of curvature of the cosmos. Take the present proper radius of the observable cosmos (45 Gly, the white circle)3 and divide it by √(Ω-1).4 This gives a radius of curvature of 45/√0.03 ≈ 260 Gly. Since we are interested in the circumference, we can multiply this by 2Pi, to get ≈ 1600 Gly. If the present universe would stop expanding abruptly, this is the minimum distance one would have to travel before you again end up where you started.

Since the universe is expanding, one can however never circumnavigate it, even if you had infinite time available. So, for all practical purposes, the total cosmos is infinite in size. Add to this that the probability for the density to be near 1.03 is quite small. It is much more likely to be closer to 1. The 95% confidence WMAP probability is Ω = 1 ± 0.01, giving a minimum circumference of around 3 trillion light-years.

As stated above, if Ω ≤ 1, the total cosmos may even be infinite today, possibly because it started out infinite in size in the first place. I still hope that it will pan out to be a finite cosmos (Ω > 1) after all.5 It will be just that little bit less mind-bending.

-J

1. I have updated the Cosmo-Calculator on my website with the new data. You can have a look at the 5-year data and the new 7-year data at the two links mentioned. Open them in separate tabs or windows for easy comparison. 7-year data from http://arxiv.org/abs/1001.4538

2. WMAP data gives the maximum values of the density parameters as: Ωm ≤ 0.29, ΩΛ ≤ 0.74, Ωtot ≤ Ωm + ΩΛ ≤ 1.03, where Ωm is the matter (normal and dark) density and ΩΛ is the vacuum energy density. We ignore radiation energy density, because when compared to the other two, it is negligible at present.

3. The yellow (28 Gly) circle shows the diameter of the observable cosmos in units of light-travel-time, not proper distance, like one would measure by a ruler.

4. It is clear that for Ω < 1, √(Ω-1) goes imaginary, signifying hyperbolic spatial curvature, like the surface of a saddle.

5. Edit: a closer look at the document http://arxiv.org/abs/1001.4538 referenced in 1 above indicates that a closed universe may indeed be slightly favored by the data. I have rounded to Ω = 1 ± 0.01, but what they say on page 17 is: 1 - 0.0084 ≤ Ω ≤ 1 + 0.0133, giving a statistical bias to the Ω > 1 case, if I'm not mistaken. It looks like a 60:40 distribution with a most-likely value at Ω ≈ 1.005. Not much, but still...

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Anonymous Poster
#1

Re: Cosmos now Bigger!

10/14/2010 8:14 AM

Wow thats a big circumference! Interesting post thanks.

www.mylocalhvac.com

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Anonymous Poster
#2

Re: Cosmos now Bigger!

10/14/2010 11:25 PM

Whew. That's a load off. I was wondering why it was taking so long. Just a question, Jorrie. We look at distant objects that suggest the visible universe - that is, the part containing star-stuff - as being what, 13.7 billion ly or so away? Then nothing. Then WMAP 'images.' Why is this? And how 'far distant' is this microwave background? I guess I'm not sure how to put all the pieces together. And, finally, Jorrie. If it all began as some primordial fireball, why isn't all of space filled with evidence of this? Is this what the WMAP data represent? Does space extend well beyond the visible? Sorry to pelt you with all these layman's questions, but I'd really like to see the whole picture, if you know what I mean. Thank you and a job well done, Sir! Just a passing Guest

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#3
In reply to #2

Re: Cosmos now Bigger!

10/15/2010 1:41 AM

Hi Guest, you asked: "We look at distant objects that suggest the visible universe - that is, the part containing star-stuff - as being what, 13.7 billion ly or so away? Then nothing. Then WMAP 'images.' Why is this?"

The 13.7 billion ly is just light-travel-distance (ltd), not present proper distance (ppd). The farthest objects that we have observed is near redshift z~10, ltd = 13.3 Gly, ppd = 31.7 Gly. There are probably galaxies too feint to observe out to z~20, ltd = 13.6 Gly, ppd = 36.1 Gly. Then nothing (galaxies not yet formed) up to the CMB at z~1088, ltd = 13.75 Gly, ppd = 45.6 Gly. This is when light and atoms decoupled and the universe became transparent, so all the microwave photons with the CMB signature (right black body temperature) that we observe come from there.

CMB photons that started from closer have passed us already and those that started from farther away have not reached us. This is the cause of the observable horizon, the white circle on the surface of the sphere above. Outside of the white circle there is an immense amount of the same, galaxies, CMB, etc, but we cannot observe there due to the limiting speed of light.

-J

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#6
In reply to #3

Re: Cosmos now Bigger!

10/15/2010 12:15 PM

"There are probably galaxies too feint to observe out to z~20, ltd = 13.6 Gly, ppd = 36.1 Gly. Then nothing (galaxies not yet formed) up to the CMB at z~1088, ltd = 13.75 Gly, ppd = 45.6 Gly."

You seem to contradict yourself. On the one hand you say that the universe is 800 billion light years in radius and on the other hand that farther than 36 billion light years there is "then nothing" :( How come?

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Anonymous Poster
#4

Re: Cosmos now Bigger!

10/15/2010 2:56 AM

Interesting to be sure. But the bigger question is what is our universe expanding into? And when will it intersect with another universe since in the cosmic all there will be other universes as there are muliple galaxies.

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#5
In reply to #4

Re: Cosmos now Bigger!

10/15/2010 6:26 AM

"What is our universe expanding into?"

The most straightforward interpretation of the data is that the universe is infinitely large and is hence not expanding into anything - an infinite thing can't get larger. It is only the space between its elements getting larger.

OK, what if 3-D space is spherical (Ω>1, as I hope it is) and hence finite in size? It still expands into nothing but itself. Think of the 2-D surface of a sphere representing our 3-D space, as in the picture above. If the sphere expands, the surface expands in the sense that there is now more surface area, but it did not expand into anything but itself. The other dimension, from the center of the sphere outwards is not part of the surface and hence not part of our 3-dimensional space.

Maybe quantum cosmology will one day come up with a credible, testable hypothesis of such other dimensions. BTW, if "other universes" do exist, they must also be in other dimensions, with no possible contact between them and us.

-J

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#10
In reply to #5

Re: Cosmos now Bigger!

10/15/2010 6:34 PM

Hi Jorrie,

As usual, an interesting blog. As for this post (#5), I disagree with much of it. However, I see no point on arguing (again) on any of it. I would not be able to prove my opinion any more than you can prove yours. Too bad human "logic" is not always logical. One of us is wrong, maybe both, sigh.

I was once criticized (not by you) for wanting the universe to be finite. Do you have a reason for this want?

Regards,

-S

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#11
In reply to #10

Re: Cosmos now Bigger!

10/16/2010 12:11 AM

Yes, the 'what is it expanding into' will probably forever be a point of debate and we must ask ourselves: does it really matter?

I have already given one reason for the my "want it finite" in the opening post: "I still hope that it will pan out to be a finite cosmos (Ω > 1) after all.5 It will be just that little bit less mind-bending. "

I also think it's analogous to 'liking' the Earth to be roughly round and not flat (with "there be dragons"), or even worse, flat and infinite. A spherical universe will be so much more mathematically tractable than a flat one, even if it is too large to ever measure it completely. I hope that I live to see future observations clearly pointing towards a closed, finite cosmos. But again, does it really matter?

-J

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#7

Re: Cosmos now Bigger!

10/15/2010 12:54 PM

There are a couple of questions I have; one is whether the cosmos is really expanding or are we just able to observe more of what is already there, with new technology and also being able to reach out farther with observation platforms like the Hubble Telescope, other satellites etc.?

What premise/s are many scientists starting from? Is it one of the Big Bang, with it's randomness, disarray and subsequent lack of evidence of a catastrophic occurence, like GUEST questioned, or is the premise one from the Creation side where there is order, predictability and design?

I believe the later premise has credibility because there is too much "wonder" in the earth around us which is available for us to study up close (that we still don't understand), let alone in the comos that we have seen and are still discovering on a continuous basis.

What we can see, and can't see yet, points to a Creator.

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#8
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Re: Cosmos now Bigger!

10/15/2010 1:31 PM

Hi facilitiesmgr, if you don't mind, I'll answer Guest (#6) together with your question.

The 36 billion light years (proper distance) 'horizon' for observing galaxies is because we are looking back in time. Before that time (~200 million years) after the BB, there were no galaxies yet. However, between 200 and 500 million years, a lot of galaxies formed, everywhere in the whole cosmos. If the cosmos is only 800 billion light years in radius, there are galaxies all the way there. We just cannot observe them...

Is the cosmos really expanding? This is a proven fact dating back to the late 1920s (Edwin Hubble). Since then it has been confirmed thousands of times by different observational methods. Do I need to say more?

As far as Creation/Creator is concerned, I think that is outside the realm of science, because it can never be proven or falsified, at least this side of eternity. The BB theory obviously does not rule out a Creator, because in its simplest form, it actually postulates a creation event, when space/time/energy all started.

I would prefer not to mix religion and science in this Blog. If you want to correspond on that, feel free to drop me a private message through the CR4 mailbox.

-J

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#9
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Re: Cosmos now Bigger!

10/15/2010 2:10 PM

"As far as Creation/Creator is concerned, I think that is outside the realm of science, because it can never be proven or falsified, at least this side of eternity." If we want to make progress in looking at facts and drawing conclusions we have to understand the scientific facts are the same for every scientist or any student. The premise that we start with are like a prism through which those scientific facts are interpreted. We will wind up with a different conclusion depending upon point we start from. The facts to interpret are the same for all of us, or it isn't science, it's opinion.

You are right in the fact that religion is involved. You can't separate science, the search for, observation and interpreting of data/facts, without seeing a source of that scientific evidence. We will either accept a Biblical account of our origin or we will accept a random account of the history of the cosmos, which is also a religious viewpoint.

You are also correct about scientifically being able to prove one way or the other until our time on earth is through.

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#12

Re: Cosmos now Bigger!

10/16/2010 8:45 AM

Jorrie, reading your title, I was amused, but not taken in, by the thought that another phase change must have taken place.

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#13
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Re: Cosmos now Bigger!

10/19/2010 12:52 AM

Hi passingtongreen, Yes, the title meant as an eye-catcher only.

It is interesting that despite all the improvements in accuracy, the maximum size still sits on the "other side of infinity" - a complex dimension (D ~ 2Pi * 45/√(-0.0084). Data do however seem to converge on a real number just "this side of infinity".

-J

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