# Is this a misleading representation of boomerang results

1. Jun 9, 2012

### jerusalem

hi,
is it misleading to write omega = 1.0000... for the ideally flat space?

2. Jun 9, 2012

### marcus

I like the illustration. It communicates a lot graphically without too much possible misinterpretation.

A picture can never tell the whole story and needs words to make sure the viewer gets the right message, but for a picture without words this does a good job, I think.

Nowadays the 2010 confidence interval for Omega is different:

0.9916 < Omega < 1.0133

So you see by modern 2010 standards the Boomerang confidence interval is WRONG.
But that is what they got, say in 1998 using Balloons in Antarctica. Now we have spacecraft in their own orbits around the sun a million miles farther out from the sun than the earth is. Of course we have better results than Boomerang. But it was an honorable well-executed attempt. And it is an excellent picture to communicate the idea.

3. Jun 9, 2012

### marcus

The neat thing is that we know the actual sizes of those fluctuations, at least as a statistical distribution, how many of each various size. And we know how far away they were when they emitted the glow that we now see. So we can estimate what ANGULAR SIZES they should have, at least as a statistical distribution, which will depend on whether space is positive curved or zero or negative.

In a positive curved space the hot-cold fluctuation patches will look BIGGER, in angular size. Like looking thru a magnifying glass. Or looking at the patch of stars behind the sun, which appears spread out because of the "gravitational lens" effect of the sun's gravity curving the rays in towards us the viewers. Making parallel rays bend in and converge.

I've seen this graphic before but I don't have a link to it. Could you give us the link? I'd like to have it handy as an illustration.

Also I have a personal reason. I think that the importance of Andrew Lange's contribution to cosmology has not been fully appreciated. He was one of the main people in charge of BOOMERANG. The concept and instrumentation were elegant. The data was surprisingly high resolution for the time (1998).

Last edited: Jun 9, 2012
4. Jun 9, 2012

### cepheid

Staff Emeritus
I don't think that the OP is questioning the veracity of the result from the BOOMERANG data (in the top panel).

It seems like the OP is asking if the Ω = 1.00000000.. statement in the lower left panel is misleading. My answer would be no, and I wonder why you think it might be. Ω is supposed to be exactly 1 for the flat case, given that you are talking the total density parameter.

5. Jun 9, 2012

### cepheid

Staff Emeritus
6. Jun 9, 2012

### marcus

Thanks!

I started a little CMB-observation history thread (Boomerang to WMAP, or could be to Planck) a while back. Anyone who knows any details of the history, of any sort, feel welcome to add. I will put your link on that thread.

7. Jun 10, 2012

### Chalnoth

I wouldn't say that. The Boomerang confidence interval was fully consistent with the current value today. We can just do better today, with many other observations.

8. Jun 10, 2012

### marcus

I'm glad you know what the interval was. Could you give a link and say what it was? This would save me having to dig it up.

The graphic which Jerusalem gave us says their estimate was [1.01, 1.13].

Is that right? Did Boomerang actually say [1.01, 1.13]?

Is that what you mean by fully consistent with the current value today, which I'm taking from WMAP7 to be [0.9916, 1.0133]?

9. Jun 10, 2012

### jerusalem

thank you cepheid,

quote: "I wonder why you think it might be"

I had an argument with some one who claimed that Ω = 1.000000.. gives a false impression about the precision of the instruments. I need to convince him that the statement in the lower left panel has nothing to do with the results of the experiment. it just states that Ω is supposed to be exactly 1 for the ideally flat space.

check this marcus arxiv.org/pdf/astro-ph/0011469v1.pdf ,, Ω = (1.07 ± 0.06)

no doubt that WMAP confidence interval is far better than boomerang confidence interval.

but my question was about the lower left panel, I wrote Ω = exactly 1 with no margin of error, since it doesn't represent the result of the experiment.

10. Jun 10, 2012

### marcus

You are quite right AFAICS. The aim of the graphic panel is to illustrate the ideally flat case where Omega is exactly 1.
At no time did I get any other impression, such as that you were saying something about the precision of the instruments.

The other person's objection does not seem reasonable or appropriate to me. I hope he can be convinced to see it in a better light.
=====================

But just as a stylistic matter you could change it to read Omega = 1
That can logically be taken to read "Omega = 1 exactly"

It communicates the essential point and it is cleaner than saying
"Omega = 1.0000000..."

When you first presented it, I did not realize that YOU had superimposed the equations on top of the Boomerang graphics. Now something you said makes me think you did, so you have control. I wonder what you are trying to get across to your audience by putting on all the zeros. Could it be communicated just as well by saying "Omega = 1 exactly"?

Last edited: Jun 10, 2012
11. Jun 11, 2012

### jerusalem

we were arguing about what Dr.Michio Kaku said here:
Dr. Tom Murphy :

ie: we should not rule out the possibility of a closed universe in a larger scale.
since we only mesure the observable universe:

12. Jun 11, 2012

### marcus

Thanks for the clarification! I happen to agree with what you highlight in red.
As I recall from the WMAP5 report, they do not even claim the observable universe is flat. They use words like "nearly flat". The data is consistent (within uncertainty bounds) with the perfectly flat model. And also it is consistent with a overall slightly curved model.

The Cornell "Ask an astronomer" site is primarily for pre-college young people, I think. Some of the language is oversimplified or not carefully enough qualified, so you have to be cautious about taking it literally sometimes. What you quoted is a case of that:

So when we say "WMAP provides strong evidence that the universe is flat", we really mean "WMAP provides strong evidence that the observable universe is flat".
curious.astro.cornell.edu/question.php?number=171​

WMAP does NOT provide strong evidence that the observable universe is EXACTLY flat.
It provides wonderfully strong evidence that Omega is in the range
0.9916 < Omega < 1.0133 (talking about the universe as a whole, assuming uniformity)

And what that translates to, in the picture of a very large balloon that looks flat to creatures living on it, is that if the curvature is at the upper limit you have a circumference of 750 billion light years (again the universe as a whole.)

That is one way of gauging the "near flatness". When you say "nearly" you suppose some way of quantifying curvedness. Most people don't grok Omega. It doesn't do anything for them to say "within one percent of unity". So you can translate that into the large balloon picture and say that the most distant matter is AT LEAST 375 billion LY away (half the circumference).

The radius of the portion we can now observe is some 45 billion LY. So the whole balloon is AT LEAST ten times bigger than what we can see---in the vague way that 375 is bigger than 45. The most distant stuff is an order of magnitude (factor of 10) farther than the most distant stuff we can see.

Or you could talk in terms of the "RADIUS OF CURVATURE" of the local patch of universe we currently see. It is one way a mathematician might quantify curvedness. Divide the circumference of 750 by 2 pi. Is that about 120?

I think I'm just repeating, but maybe that doesn't hurt. We don't have, in our common everyday language, good ways to talk about degrees of curvedness. But to give an honest account of what is known (WMAP and also BAO and SN data) we have to have a way. We can't just say "flat" and give the listener the idea of EXACTLY flat. We have to say nearly, and that supposed a concept of amount of flatness or curvedness.

If you like the idea of a "radius of curvature" then 2010 WMAP report says that RoC of the patch of universe we can see is, with 95% confidence, at least 120 billion LY

that is the radius of the fitting hypersphere, if the observable patch were laid on the 3D "surface" of a fitting 4D hypersphere.

13. Jun 11, 2012

### Chalnoth

Actually, I don't remember the specific parameters off the top of my head. I was, in part, going by the numbers posted earlier in this thread. I know, however, that no experiment to date has detected a statistically-significant deviation of spatial curvature from zero.

If you're curious, though, here is their paper on cosmological paramters for their latest flight (2003):
http://arxiv.org/pdf/astro-ph/0507503v1.pdf

There are multiple ways to combine the data, but the curvature always deviates from zero at less than two standard deviations.

14. Jun 11, 2012

### Chronos

As I recall, boomerang allowed a generous range for omega - ranging from about 0.8 to 1.3. The 1.01+ thing was merely a best guesstimate.

15. Jun 12, 2012

### Chalnoth

Well, you generally don't get a very tight range using only CMB data. But combine Boomerang with other data and the constraints close to a couple percent (as shown in the paper I linked above).

Still that's rather old. We have better data today. Boomerang was just one experiment among a great many.

16. Jun 12, 2012

### cepheid

Staff Emeritus
I don't think that is the case. I'm pretty sure that the constraints are somewhat tighter than that. As described here:

http://arxiv.org/abs/astro-ph/0104460

and in the paper they reference by Lange, 2001, they do a likelihood analysis, and the best estimate of the parameter is obtained from the peak of the likelihood function, with the uncertainties obtained by integrating over this function out to the 1-sigma limits. Maybe this is what you meant by best guesstimate, I don't know. They have values reported in table 5 such as 1.02 +/- 0.06, or 0.98 +0.04, -0.05, depending on their choice of prior.

17. Jun 13, 2012

### jerusalem

is there a degree of precision, if reached, we can say for sure that we are living in an infinite euclidean space?
well my interlocutor refused this possibility and claimed that (boomerang and wmap..) measure the shape of the ENTIRE universe because the photon we detect started its journey since the beginning (380000 after BB). Did you ever heard such interpretation ? In my opinion this make sense only if the speed of light is greater than the expansion of the universe.

18. Jun 13, 2012

### Chalnoth

No. That would require infinite measurement accuracy, which is impossible (not just because building an infinitely-accurate measurement is impossible, but also because we can only see a fraction of the whole universe).

No, they only measure the shape of the visible portion of it. Extrapolating beyond the region which is visible to us is highly model-dependent.

19. Jun 15, 2012

### jerusalem

Thank you guys for your replies

20. Jul 12, 2012

### Ibrahim64

Hello
I was in discussion with Mr jerusalem about the universe did not require energy to form. I used Boomrang experiment since its results are freely available and can show the scientific result. I presented paper: http://arxiv.org/pdf/astro-ph/0011469v1.pdf, which shows that the results and made an estimate of Ω.
The experiment showed that the flat universe is in the confidence interval and I said that since the flat universe is in intersection between Boomrang experiment and Adams' Rees SN1a Measurement, then this experiment corroborate the hypotheses that the universe is flat. I told Mr jerusalem that, $Ω= 1$ is not real, but is a valid classical approximation because
paper: "the size and shape of the universe: The quest for the curvature of space" states that:$\frac{C^2}{R^2}=H^2(Ω-1)$
and a theory involves Quantum mechanics and general theory of relativity will remove the singularity at the begging of the universe and the infinite size of the universe.
The problem is:
1. Is it valid to take middle of the range? or if there is a theory predict a value we say that the experiment corroborate the hypotheses?
2. Is it valid to place 8 zeroes with experiment result that never claimed more than %15 accuracy...
These discussion has been for a while, Mr jerusalem tries to discredit me by making all of these misrepresentation of my actual saying. As you can see in the figure attached, Mr jerusalem took the value in middle and put it the actual result.
The figure under discussion was:

is this valid representation of Boomrang result or WMAP result?
Regards
Dr Ibrahim

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Last edited: Jul 12, 2012