Will the new WMAP3 data challenge the assumption of a spatially flat universe?

[wolram]

What maths are you talking about? The observational evidence, taken in full, does not put flatness outside the one-sigma error bars and we certainly aren't 68% confident that the universe is closed. I can assure you that the astronomical community doesn't consider the curvature measurement an "enigma". As for the future, high-precision measurements of the curvature might turn out to be interesting, but w is likely going to be the focus in the next 10 or 20 years.

I am very sorry i some what hi jacked Marcus,s thread, i wil bow out and
leave the question, to ,you whow know better

 

[SpaceTiger]

I am very sorry i some what hi jacked Marcus,s thread, i wil bow out and
leave the question, to ,you whow know better

Nonsense, you're more than welcome to contribute, I just want to make it clear that the flatness issue is not being emphasized by the community at the moment and most (to my knowledge) don't view the measurements of flatness as being inconsistent with standard theory.

I'm just reporting the mainstream view here -- that's not necessarily the "correct" view, but it's probably the most reliable. Everyone is free to their opinion and debate is welcome on PF, I just don't want to give people the wrong impression about what the members of the WMAP team are saying. I know we're all eager to pull something exciting and revolutionary from these data, but I think it's wise to exercise some restraint, especially if our ideas run contrary to the views of the experts.

As marcus has already said, there will be a lot of discussion on this in the coming months and years, so the mainstream view may shift. I doubt, however, that it will shift very much. Spergel, Page, and company are highly respected and, as with the first release, I expect that the majority of their conclusions will be taken as the most reliable until more data become available.

 

[marcus]

I am very sorry i some what hi jacked Marcus,s thread, i wil bow out and
leave the question, to ,you whow know better

Indeed you did not hijack, Wolram!

You elicited exactly the right sort of comment on what mainly concerns me in this thread! As you can see, Nick's opinion about the mainstream or "community" view differs slightly from mine. I see the view in mainstream cosmology as less consistent and more mutable than he does. Which is fine. Neither of us are, I believe, cosmologists and even a professional cosmologist might not be able to report with absolute certainty!

In a nutshell, the figure 17 on page 50 of the paper suggests the possibility that the U may be closed (i.e. spatial finite, pos. curved). However this is not the only figure or table in the paper, and there are several ways to analyze the data. It would be a good idea to actually compare some of the other things like table 11. I looked at table 11 several days ago and did NOT find it in stark contrast with figure 17.
the results always vary a little depending on what data sets are combined with WMAP and on the actual analysis performed. We could look at that again.

In any case the academic tradition is that NO one person speaks for the "official" consensus or for the community. We each have the right to our opinion. My opinion is that a finite pos curve universe is a serious possibility----something I want to discuss and understand better.

Indeed what I wish to emphasize and study very carefully in this thread is the possibility, clearly evinced by the WMAP data and by this "implications" paper, that the U is closed. I think Nick put it very nicely.

Essentially "closed" means that the true value of Omega is, with some nonzero probability (like 68 percent), inside some errorbar range which is bounded away from one. Like for example [1.008, 1.037].

I don't know whether I BELIEVE figure 17. But I want to understand better what the consequences are if something like that turns out to be correct. I don't want to simply dismiss it out of hand because it is novel or unfamiliar.

In the past it has often been assumed that Omega = 1 or that whenever we measured it we would always get some errorbar for it that was around 1------like for example [0.995, 1.005]----so then we could not rule out the case where it exactly equals one, nor could we rule out other cases, like it is a tiny bit positive.

People are accustomed to that situation, where the data is consistent both with infinite and finite cases, with flat and with non-flat. Officially that is still the situation but I sense a possible change in the wind.

 

[SpaceTiger]

I've tried to avoid arguing with you directly because I know it makes you uncomfortable, but the majority of your last post was effectively in response to me, so I think it's called for now.

Neither of us are, I believe, cosmologists and even a professional cosmologist might not be able to report with absolute certainty!

Do you not count cosmology graduate students as cosmologists? Forgive me. Perhaps you would prefer the word of David Spergel, Paul Steinhardt, or Lyman Page, each of whom actually presented these results to us on the day of the release and each of whom played a part in training me. They gave no indication that the data should be taken as implying a non-flat universe (again, at this precision).

I looked at table 11 several days ago and did NOT find it in stark contrast with figure 17.

Considering that all but one of the other data sets brings the curvature estimate down so that flatness is within the one-sigma confidence interval, I'm curious to know what your definition of "stark contrast" is.

In any case the academic tradition is that NO one person speaks for the "official" consensus or for the community.

Perhaps you would prefer the term "majority view" rather than "mainstream", though I think they're both suggestive of the same thing. I don't recall using the word "official". The only sense in which my position is "official" is that it's the position of the WMAP parameters paper. I don't know how others will interpret it, but unless there arise new methods of analysis that point more strongly to a closed universe, there's no reason to think that their position will be seriously questioned. I doubt the measurement will be ignored, that is, you might see some discussion of it on arxiv, but I can assure you that the majority will need more than this to favor a closed model.

But I want to understand better what the consequences are if something like that turns out to be correct.

This, I think, is a much better topic of discussion. Bickering over the WMAP error bars is not going to go anywhere productive.

I don't want to simply dismiss it out of hand because it is novel or unfamiliar.

A closed universe is far from novel or unfamiliar, even in the inflationary paradigm. In fact, it's one of the first models taught in intro cosmology classes. What gave you the impression that it was "novel"?

My opinion is that a finite pos curve universe is a serious possibility----something I want to discuss and understand better.

You keep changing the phrasing your opinion to make it sound like I'm saying something ridiculous. I've said several times that a closed universe is a serious possibility, what I object to is your assertion that they are "68% confident that the universe is not flat".

 

[marcus]

Do you not count cosmology graduate students as cosmologists?
...

You decided to specialize in cosmology! Great! Last time i remember you saying anything about that, as i recall you said your room-mate was into cosmology but not you. I may be misremembering. In any case I congratulate you.

Sorry I didnt know you had picked cosmology. Just knew you were in astro at P.

Still don't think you can report more than your opinion about the mainstream or professional consensus. There is no official "party line" is there?

I respect your opinion, your take on the community view, as such. I have my own sense of it.

Have to go, be back later.

 

[marcus]

Ways I could be wrong

Basically I like to report on mainstream cosmology. So I have a take on it. No matter whose take, it is just opinion (there is no official spokesperson) so my take on the current situation could easily be wrong! As an exercise (and reminder of fallibility) I will try to list some ways that my view might turn out to be wrong

1. I expect a nuanced shift in how cosmologists talk about the finite/infinite, flat/nonflat issue over the coming months. If that doesn't happen, then I was wrong.

I am hardly ready to call it yet, but remember that Spergel et al, in their conclusions, said the data was consistent with a "nearly flat" universe. they could easily have said flat because in a cruder sense it IS consistent with a perfectly flat case----the data does not yet exclude that. but they didn't

that might or might not be the beginning of a nuanced shift, time will tell

2. I think it will be useful to get accustomed to thinking about and discussing the non-flat case, as one of the possibilities. So I invite discussion. What, if anything, is special about a finite (as opposed to infinite) universe?
If after learning a bit about these things and talking it over, it turns out NOT to have been useful, that will show me wrong.

I have to go, busy just now, I will try to think of different ways I could be wrong and add them to the list.

 

[Chronos]

. . . but w could easily be changing with time, perhaps asymptoting to -1 at the present epoch. If their assumptions for w are wrong, then the consequences wouldn't necessarily just manifest themselves in w, they could also appear in the best-fit values of the other parameters, including the curvature.

Quite frankly, I think the vanilla cosmological constant model is going to turn out to be wrong.

I think w has changed over time, which seasons, but does not entirely discredit the vanilla model. Accelerated expansion in the recent epoch suggests this, as well as [albeit to a lesser extent] inflation in the early universe.

The most gratifying result of Y3 [to me] is nailing down the third peak in the power spectrum. This, I believe, really solidifies the concordance model. When you combine it with other recent, monumental studies, like SDSS, it looks bullet-proof. We live in exciting times. While not yet fully appreciated [again IMO], WMAP is the modern day equivalent of GR.

 

[Garth]

The most gratifying result of Y3 [to me] is nailing down the third peak in the power spectrum. This, I believe, really solidifies the concordance model. When you combine it with other recent, monumental studies, like SDSS, it looks bullet-proof. We live in exciting times. While not yet fully appreciated [again IMO], WMAP is the modern day equivalent of GR.

But it wasn't WMAP3 that 'nailed down' the third peak, as you can see here (You have to press <Page Down> once, or click on the first page), a series of lecture slides by Antony Lewis of the IoA, Cambridge, England. That second slide shows the power spectrum and the WMAP3 data with Acbor, Boomerang, CBI & VSA readings superimposed.

Whereas those other experiments do trace the predicted third and even fourth peaks and beyond fairly well, the WMAP3 data does not. In particular the errors bars at l= ~870 and beyond do not even reach the predicted curve. At the third peak and beyond the other experiments are used to 'nail down' the comparison of observation with prediction.

Note in the discussion about flatness that there is a 'prior' that is so taken for granted that it is not even acknowledged: the analysis assumes GR and therefore a Friedmann model. Consequently the appearance of flatness requires \Omega_t = 1 and GR BBN requires \Omega_b = 0.02 - 0.04.

However, the first peak is consistent also with conformal flatness that may be delivered by a modification of GR. Best keep the options open...

Garth

 

[SpaceTiger]

You decided to specialize in cosmology! Great! Last time i remember you saying anything about that, as i recall you said your room-mate was into cosmology but not you. I may be misremembering. In any case I congratulate you.

I haven't graduated yet, so there's no reason for congratulations, but I have been working on a thesis in cosmology for the last two years. I may have reported working on other things because we're required to do "semester projects" in a variety of areas. My roommate, quite the contrary, is working with planets and didn't even attend the WMAP talk. Some people, you know.

Still don't think you can report more than your opinion about the mainstream or professional consensus. There is no official "party line" is there?

If you object to the use of the word "mainstream" as sounding too general, then I'll say again, majority view. I can report the majority sentiment in this department and with less certainty the majority sentiment outside of it.

I'm not implying that anyone who suggests a non-flat universe is a crank, if that's what you're concerned about. It will be good to see if inflation can produce non-flatness at this level, just in case the high value of curvature holds. I'm pretty sure it requires fine-tuning, however, so given the confirmed predictions of inflation in other areas, I think people will need more before they start favoring a closed universe.

 

[SpaceTiger]

1. I expect a nuanced shift in how cosmologists talk about the finite/infinite, flat/nonflat issue over the coming months. If that doesn't happen, then I was wrong.

Could you be more specific? I'm not even sure what that means. I would not be surprised to see papers addressing the issue (there were some of those even after the first release), but that doesn't mean the majority has shifted to believing in a positively curved universe.

I am hardly ready to call it yet, but remember that Spergel et al, in their conclusions, said the data was consistent with a "nearly flat" universe. they could easily have said flat because in a cruder sense it IS consistent with a perfectly flat case----the data does not yet exclude that. but they didn't

Actually, as I already pointed out, they did, at the end of the section on non-flatness. Again, this implies to me that you're reading too much into their words.

2. I think it will be useful to get accustomed to thinking about and discussing the non-flat case, as one of the possibilities. So I invite discussion. What, if anything, is special about a finite (as opposed to infinite) universe?

This is more of a philosophical question than a scientific one. Physicists and astronomers have traditionally tried to avoid invoking infinities in their calculations, so I think there is a natural preference towards a finite universe.

Theoretically, we expect curvature to manifest itself at levels consistent with the inflationary scenario. If they became apparent at the current precision of WMAP, it would require either a fine-tuning of inflation or an alternative theory.

 

[SpaceTiger]

Note in the discussion about flatness that there is a 'prior' that is so taken for granted that it is not even acknowledged: the analysis assumes GR and therefore a Friedmann model. Consequently the appearance of flatness requires \Omega_t = 1 and GR BBN requires \Omega_b = 0.02 - 0.04.

Yes, though it should be noted that others have done an analysis of the CMB using relativistic MOND instead of GR. The problem of the third peak persists, mainly because you need an entirely separate forcing term between baryons to produce it.

 

[marcus]

...It will be good to see if inflation can produce non-flatness at this level, just in case the high value of curvature holds...more before they start favoring a closed universe.

Could you please spell out what you mean in more detail. what inflation model(s)?
My memory from Lineweaver's paper a couple of years back (Inflation and the CMB) and subsequent things I've seen is that inflation FLATTENS OUT an already curved situation

Guth orig (1981 IIRC) paper was about inflation as a solution to the "horizon problem" and the "flatness problem".

you speak of inflation PRODUCING some degree or level of non-flatness.

Naive question: please clear up the apparent contradiction

majority cosmologists do not YET at this time favor closed (I agree BTW which is why I find the matter so interesting, I sense possibility for a shift in majority opinion) OK, so they don't favor closed.

Now they do like to think about a situation that started out curved, non-flat, and that inflation FLATTENED OUT.

So isn't the initial picture of something that is NOT CLOSED, not spatially finite, and nevertheless curvy? Please clarify what the common initial picture is. Is the initial U spatially infinite but just has some random bumps? Is it these random bumps that inflation flattens out?

Basically, I'd like you to say more about your words
"if inflation can produce non-flatness at this level, "

is the context for that "if" a spatially finite U, or not?

====================
[EDIT, I JUST SAW THIS]
"Theoretically, we expect curvature to manifest itself at levels consistent with the inflationary scenario. If they became apparent at the current precision of WMAP, it would require either a fine-tuning of inflation or an alternative theory."

That is interesting. What is an arxiv paper that discusses this and calculates what level of curvature IS consistent with some favored infl. scenario?

Is the estimate robust, i.e. does it depend simply on some estimate of the number of e-foldings?

 

[SpaceTiger]

Could you please spell out what you mean in more detail. what inflation model(s)?
My memory from Lineweaver's paper a couple of years back (Inflation and the CMB) and subsequent things I've seen is that inflation FLATTENS OUT an already curved situation

You're correct, perhaps I should have chosen my words more carefully. The question is whether or not one can produce an inflationary model that doesn't flatten the universe beyond the limits this experiment can detect. We have constraints on the duration of inflation, as I said earlier, and thus the amount of "flattening".

So isn't the initial picture of something that is NOT CLOSED, not spatially finite, and nevertheless curvy?

The initial picture is unknown. The point is that inflation produces a nearly flat universe, regardless of initial conditions.

That is interesting. What is an arxiv paper that discusses this and calculates what level of curvature IS consistent with some favored infl. scenario?

Is the estimate robust, i.e. does it depend simply on some estimate of the number of e-foldings?

Here's a nice paper on the issue:

http://arxiv.org/abs/astro-ph/0503405"

We expect non-flatness to be detectable at the level of:

\Omega_kh^2\sim 10^{-5}

 

[marcus]

Here's a nice paper on the issue:

http://arxiv.org/abs/astro-ph/0503405"

We expect non-flatness to be detectable at the level of:

\Omega_kh^2\sim 10^{-5}

Thanks! I love getting arxiv references, some I can follow or follow parts of, some i cant. but it all helps one way or another.

that 10^-5 seems way far away
because IIRC h is .73 or order 1 and therefore if I am not mistaken that is saying that Omega_k is order 10^-5

but now we are only seeing stuff order 0.01 and 0.001, too bad

not time to look at Knox right now but will get to it soon.

 

[Nereid]

A general question (or three) about this thread - has the main WMAP3 thread superceded the need for this, separate, thread (so we can close it, and continue discussions in the main one)? If not, what should the title of this thread be changed to (it's present title is rather inappropriate, n'est pas)?

 

[marcus]

A general question (or three) about this thread - has the main WMAP3 thread superceded the need for this, separate, thread (so we can close it, and continue discussions in the main one)? If not, what should the title of this thread be changed to (it's present title is rather inappropriate, n'est pas)?

I am interested in focusing in this thread on the issue of Omega possibly being greater than 1, and the spatial slices of the universe being closed----finite.

I would like very much to keep this thread open so that I can discuss whatever new stuff comes in on that.

There are a lot of other interesting issues regarding the WMAP3 data, so I want a thread focused on this one issue so it does not get drowned out by wideranging discussion of other stuff.

It would be rather a lot of work for me to start a new thread on the focus issue, so I would much prefer to keep this one open for that reason too.

If you have some ideas for renaming, I would like to hear them! Maybe you could send me a PM

 

[marcus]

more stuff bearing on spatial closure

A noted cosmologist George Ellis (coauthor with Stephen Hawking of The Largescale Structure of Spacetime has been invited to contribute a chapter on Cosmology Issues to a new Elsevier Handbook
and has posted a 60 page essay, in which he devotes some attention to the finiteness or spatial closure issue

See pages 18 and 25 of this
http://arxiv.org/abs/astro-ph/0602280
Issues in the Philosophy of Cosmology
George F. R. Ellis
To appear in the Handbook in Philosophy of Physics, Ed J Butterfield and J Earman (Elsevier, 2006)

"After a survey of the present state of cosmological theory and observations, this article discusses a series of major themes underlying the relation of philosophy to cosmology. These are: A: The uniqueness of the universe; B: The large scale of the universe in space and time; C: The unbound energies in the early universe; D: Explaining the universe -- the question of origins; E: The universe as the background for existence; F: The explicit philosophical basis; G: The Anthropic question: fine tuning for life; H: The possible existence of multiverses; I: The natures of existence. Each of these themes is explored and related to a series of Theses that set out the major issues confronting cosmology in relation to philosophy."

It is clear that the book is intended to be a standard reference work for research professionals including cosmologists. I think Ellis does a fine job clearly delineating a number of issues that cosmology may address and help resolve.

Because in this thread I wish to focus on the spatial closure issue (and a possible shift in how working cosmologists treat the issue as fresh data appears) I will quote some from relevant passage of Ellis essay.

 

[marcus]

Ellis list of common misconceptions, page 18

In section 2.8.1 page 18 he has this list of misconceptions. I do not suggest that anyone here at PF suffers from the listed misconceptions. I quote an exerpt because it has some interesting stuff.
====exerpt=====
...
...
Misconception 5: The space sections are necessarily infinite if k = 0 or -1. This is only true if they have their ‘natural’ simply connected topology. If their topology is more complex (e.g. a 3-torus) they can be spatially finite [49, 130]. There are many ways this can happen; indeed if k = -1 there is an infinite number of possibilities.

Misconception 6: Inflation implies spatial flatness (k = 0 if and only if Omega = 1) exactly. There is nothing in inflationary theory which determines the sign of the spatial curvature. Inflationary universes are very nearly flat at late times; this is very different from being exactly flat (a condition which requires infinite fine tuning of initial conditions; if say the two millionth digit in the value of Omega is non-zero at any time, then the universe is not spatially flat).

Inflationary theory does not have the theoretical teeth required to imply that the universe has exactly flat spatial sections; hence a key issue for cosmology is observationally determining the sign of the spatial curvature, which is potentially dynamically important in both the very early universe [80, 72] and the late universe (it determines if recollapse is possible, should the dark energy decay away).
========endquote=====

 

[SpaceTiger]

Misconception 6: Inflation implies spatial flatness (k = 0 if and only if Omega = 1) exactly. There is nothing in inflationary theory which determines the sign of the spatial curvature. Inflationary universes are very nearly flat at late times; this is very different from being exactly flat (a condition which requires infinite fine tuning of initial conditions; if say the two millionth digit in the value of Omega is non-zero at any time, then the universe is not spatially flat).

That's right. As was explained in the other paper I linked, the primordial power spectrum that arises from inflation (nearly scale invariant) predicts deviations from flatness at about the 0.001% level. This doesn't say anything about the sign of the curvature, just the magnitude of the random fluctuations at that scale. Since the fluctuations are theorized to be random, we could be living in an overdensity, underdensity, or average part of the universe. However, if the universe were overdense or underdense by a very large amount (i.e. flat or non-flat at levels beyond that precision), it would be very suspicious and possibly indicate that there is a problem with the standard model.

 

[marcus]

... scale invariant) predicts deviations from flatness at about the 0.001% level. This doesn't say anything about the sign of the curvature, just the magnitude of the random fluctuations at that scale. Since the fluctuations are theorized to be random, we could be living in an overdensity, underdensity, or average part of the universe. ...

Thanks for your comment.

I looked at the Knox paper and I interpret it to mean that even if the universe is not spatially closed it might have random fluctuations in curvature local to our observable part of it that are on the order of 10^-5 in Omega

that is + or - 0.00001

so we are talking about a possible observation of, say, Omega = 1.00001.

I think this is in line with what you are saying, you say A THOUSANDTH OF A PERCENT which is just the 0.00001 or the 10^-5 that Knox says.

I won't be thinking of Omega = 1.00001 as a condition that would imply spatial closure.

I think you probably agree, if I understand what you say.

the topic of the thread here, and what I want to consider, is the possibility left open by WMAP3, which future measurements could confirm, of a much larger positive curvature---like Omega = 1.01----and a universe with closed spatial sections (as all know that could also occur in the flat case with special topology so substantial positive curvature is just one possible condition implying what we are talking about)

have to go, but will be back later

 

[marcus]

I have some quotes from Ned Wright (the cosmologist at UCLA whose website and its cosmo. tutorial many of us have visited) and from George Ellis that I want to put in.

this will help give an idea of what some selected people are saying now and later on we can see if there has been any significant shift in the message.

Here is George Ellis on page 25 of his "Cosmology Issues" essay
====exerpt=====

4.2.3 Determining the RW parameters [Robertson-Walker]

Given that a RW geometry is a good description of the observable universe on a large scale, the further issue is what are the best-fit parameters that characterize it, selecting the specific universe we observe from the family of all FL models (Sec.2.1). Important observational issues are:

• Determining the Hubble parameter H_0, which sets the overall scale of the observed universe region.

• Determining the trio of the density parameter Omega_0, deceleration parameter q_0, and cosmological constant Lambda (or equivalently the density parameter Omega_Lambda), which are the major defining characteristics of a specific Friedman-Lemaitre model. The CBR data, supernova observations, deep number counts, source covariance functions, velocity measurements, and gravitational lensing observations can determine these quantities.

• Determining the sign of the curvature k, showing whether the universe has closed spatial sections and also whether it is possible for it to recollapse in the future or not. Analyses of the observations should always attempt to determine this sign, and not assume that k = 0 (as is often done).

• Various parameters are used to characterize the nature of dark matter (Sec.2.3.6) and dark energy (Sec.2.3.5). As their dynamics is unknown, these too have to be determined observationally.
=====endquote=====

It seems to me that Ellis is critical of some of his fellow cosmologists for favoring the SPATIALLY NON-CLOSED picture to such an extent that, according to him, they "often" TAKE IT FOR GRANTED. This is how I understand what he says here.

Interestingly enough today Ned Wright posted something on arxiv that sends a similar message. Let me get it.

 

[marcus]

what Ned Wright posted today

Conceivably someone reading this thread might be interested by what Ned Wright had to say about this in something he put on arxiv today:
http://arxiv.org/abs/astro-ph/0603750
A Century of Cosmology
E. L. Wright (UCLA Astronomy)
Talk presented at the "Relativistic Astrophysics and Cosmology - Einstein's Legacy" meeting in Munich, Nov 2005. Proceedings will be published in the Springer-Verlag "ESO Astrophysics Symposia" series. 10 pages with 2 figures

AS ONE OF HIS FIGURES Wright has a caricature of a cosmologist's CIRCULAR ARGUMENT: It is his Figure 1. A big circle of words evidently meant as a joke. It has these words going around the circle:

"If w = - 1, then flat LambdaCDM is a good fit to all the data. If Omega = 1 , then w = - 1 is a good fit to all the data.[/color]"

He is opposed to assuming flat. Explaining this Figure 1. he says
"However, there is a very strong tendency among theorists to assume the Universe is flat when seeking w and w'. This is a logical error, since the evidence for a flat Universe comes from the agreement of the concordance LambdaCDM model with all the data. But the concordance LambdaCDM model has w = -1 and w' = 0 exactly. If w and w' are allowed to vary, then the evidence for a flat Universe must be re-evaluated. ... "

Unfortunately I have to go out now so can't finish this post but will get back to it later.

========
I'm back now. Yeah. I think to put it simply the message of what Wright says, and of his figure 1, is that IT IS NOT COOL ANYMORE TO ASSUME FLAT.

Wright is a leading cosmologist, in case any reader doesn't know----he was one of a group of top scientists in charge of WMAP----so you see his name as co-author on some main WMAP papers. But he was an important figure already before that.

=========

Eventually I will get over to the Astronomy building and talk to some grad students---in the coffeeroom or in one of their offices. So far I am going on signals i get from bigname people like George Ellis and Ned Wright, and from things like Figure 17 of the Spergel et al paper. But I would also like to talk with some of the "troops on the ground". Over the years I've done that on occasion and they (random grad students) have been very helpful. that should give additional perspective on a possible shift.

 

[Chronos]

Marcus, I agree in spirit with Ned Wright's analysis, but am reluctant to accept the conclusion. There are too many conflicting observations that cannot be ruled out. Maybe, in 100 years, the answer will become obvious. For now, I cannot accept that assertion.

 

[marcus]

Marcus, I agree in spirit with Ned Wright's analysis, but am reluctant to accept the conclusion. There are too many conflicting observations that cannot be ruled out. Maybe, in 100 years, the answer will become obvious. For now, I cannot accept that assertion.

You are heartily welcome to whatever your attitude is but I don't understand what you think is his "conclusion" or his "assertion" that you say you can't accept.

Wright is a working cosmologist who was involved in the planning execution of WMAP and in the analysis of WMAP3. He is talking about what to do TODAY, not in 100 years. Nothing visionary here.

He says that if you want to find out about w, then you should let BOTH w and Omega VARY SIMULTANEOUSLY and use the data to constrain both.
He says that you should not peg Omega = 1 and then calculate w

and he says you should not peg w = -1 and then calculate Omega.
He says, to put it simply, IT IS NOT COOL TO ASSUME FLAT i.e. to assume Omega = 1.

this could be seen as just good scientific advice to people doing analysis of data today and tomorrow.

He actually goes further and says that you should let w AND its timederivative w' AND Omega vary and try to constrain them all. To allow for the possibility that w could be changing. But the simple version of the message is to let Omega and w vary----which incidentally was what was done in Figure 17 of Spergel et al, the figure which I liked so much and discussed earlier in this thread. That Figure illustrates a simple version of what Wright advocates doing.

Wright makes this the message of his Figure 1 , and his conclusions paragraph, of the paper he put on arxiv yesterday.

I'm happy for you to be as reluctant as possible but I just want to make sure we are on the same page and both talking about the same conclusions of the same Ned Wright paper! As long as we understand what we're talking, then I'm delighted if you have a negative reaction. It illustrates what I think is a majority, or at least very common, attitude in the field----and one which Wright is addressing---and one which I think will gradually shift over the coming little while. We will see

 

[marcus]

As could be expected, since Ned Wright is a key figure in this whole business, and one of the WMAP project leaders, he is one of the co-authors of the "Implications for Cosmology" paper which is the basis for this thread.

this is the paper we call "Spergel et al".
I should put the link again, in case someone drops into this thread and wants to look at the WMAP3 results "implications for cosmology"

http://arxiv.org/abs/astro-ph/0603449
Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology

the Figure 17 is on page 50 IIRC, in case anyone wants to check it out

 

[SpaceTiger]

I attended a talk yesterday in which the speaker was discussing future methods of measuring curvature and dark energy parameters. In the next ten or twenty years, they expect to be able measure curvature to at least one more decimal place and perhaps two. The seemingly best method of doing this is with weak lensing surveys, but Type Ia supernova, cluster counting, and baryon oscillation experiments should do comparably well.

He also discussed methods of actually testing GR (which would be refreshing) by measuring dark energy parameters and then comparing the predicted and measured growth functions, which describe the growth of perturbations in a general relativistic universe.

In the middle of his talk, he flashed up your favorite graph from the WMAP3 paper, but gave no indication that he thought it was suggestive of a universe with positive curvature.

 

[marcus]

I attended a talk yesterday in which the speaker was discussing future methods of measuring curvature and dark energy parameters. In the next ten or twenty years, they expect to be able measure curvature to at least one more decimal place and perhaps two...

COOL!

In the middle of his talk, he flashed up your favorite graph from the WMAP3 paper, but gave no indication that he thought it was suggestive of a universe with positive curvature.

Fine, in a certain sense that gives us a kind of benchmark for where people's heads are, at the moment. I should really go talk to some of the local grad students. that will also give a benchmark, I can then come back later and gauge if any change.

 

[marcus]

another straw in the wind?

I don't recommend this article---on the contrary: apologize for even mentioning it---and so wrote the mention in white

http://arxiv.org/abs/astro-ph/0603690
Cross-correlation of WMAP 3rd year and the SDSS DR4 galaxy survey: new evidence for Dark Energy
A.Cabre, E.Gaztanaga, M.Manera, P.Fosalba, F.Castander (IEEC/CSIC)
5 pages, 5 figures, submitted to MNRAS Letter
We cross-correlate the third-year WMAP data with galaxy samples extracted from the SDSS DR4 covering 13% of the sky, increasing by a factor of 3.7 the volume sampled in previous analyses. The new measurements confirm a positive cross-correlation with higher significance (total signal-to-noise of about 4.7). The correlation as a function of angular scale is well fitted by the integrated Sachs-Wolfe (ISW) effect for LCDM flat FRW models with a cosmological constant (w=-1). The combined analysis of different samples gives Omega_L=0.75-0.80 (68% Confidence Level, CL) or 0.70-0.82 (95% CL). We find that the best fit Omega_L decreases from 0.82 to 0.75 (95% CL) when we increase the median redshift of the galaxy sample from z~0.3 to z~0.5. The quick drop of the measured signal with z is too fast for the LCDM cosmology. The data can be better reconciled with a model with an effective dark energy equation of state w<-1.5. Such phantom cosmology reduces by up to ~20% the amplitude of the lower multipoles of the CMB temperature anisotropies with respect the w=-1 prediction, which also brings the models closer to the observations.[/color]

I find the idea of w<-1 repugnant, as do all rightthinking ppeople I would hope. there is a strong appeal of the two ideas w = -1 exactly and Omega = 1 exactly (or 1 with a little random quantum ripple).
However these people (Spaniards, I see) find something about the WMAP3 data suggests to them w way less than -1. Even in my favorite Spergel figure 17 the 68% confidence interval for w only goes down to -1.14 and they are below that. Yuk. Is this a sign of the times?

=========================
the main paper we are assimilating in this thread is "Spergel et al", the "implications for cosmology" paper that has Ned Wright as a co-author.
I should put the link again:

http://arxiv.org/abs/astro-ph/0603449
Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology

Have another look at Figure 17 is on page 55 IIRC, to see what it would mean to contemplate the unpalatable idea that w might be less than -1.

 

[Chronos]

The best fit models proposed by Spergal et al. still suggest, without insisting that w is very close, if not exactly -1. I think that is just good science.

 

[marcus]

The best fit models proposed by Spergel et al. still suggest, without insisting that w is very close, if not exactly -1.

that is right. Personally I tend to assume w=-1 exactly, which would be consistent with a positive curved, spatially closed, finite, universe if you favor that picture. And also consistent with other cases as well! Essentially it just means that the dark energy corresponds to Einst. cosmological constant. But my liking to assume w=-1 is a personal bias which I try to discount and avoid infecting my judgment. One reason I do this is because of what Ned Wright says.
https://www.physicsforums.com/showpost.php?p=949832&postcount=72
http://arxiv.org/abs/astro-ph/0603750

...that is just good science

One of my guides regarding "good science" is Ned Wright, and he says to let w and Omega (and maybe even w') vary simultaneously. that is, when you are trying to estimate w (the DE EOS) you should not make any assumption about the universe being flat or not. Although the darkenergy EOS is nominally separate from flatness or spatial closure issues, they can influence each other in the calculation, so it should be treated that way when you analyze. One should make an effort to avoid prejudice about Omega when one estimates w-----in other words let them both vary simultaneously and constrain both.

In a nutshell, he says "do not peg Omega = 1 when you estimate w, and do not peg w = -1 when you estimate Omega" because they both might not be those numbers and pegging can skew the fit.

So the kind of analysis that results from doing what he says is Figure 17 on page 55, and here is a quote from the caption:

The contours show the 2-d marginalized contours for w and Omega_k based on the the CMB+2dFGRS+SDSS+supernova data sets. This figure shows that with the full combination of data sets, there are already strong limits on w without the need to assume a flat universe prior. The marginalized best fit values for the equation of state and curvature are w = -1.062 (+0.128 -0.079) and Omega_k = -0.024 (+0.016 -0.013) at the 68% confidence level.

What that says about w is that at 68% confidence it is in the interval
[-1.141, -0.874]

That is the darkenergy EOS is in an interval AROUND -1, and estimate varies roughly on the order of TEN PERCENT around -1.

this is how i might make sense if someone says " w is very close, if not exactly -1"
I don't object if they want to say it that way. In some contexts, on some days, if I am feeling right, I also would say that roughly 10% is "very close, if not exactly"

And because of my confessed bias, I am quite happy with that 68% interval around w = -1. So fine! All well and good.

But this does not say anything about SPATIAL CLOSURE, does it Chronos?

For that, if one is following Ned Wright's guidelines for good science and allowing both w and Omega to be constrained simultaneously, one gets the 68 % confidence interval for Omega which is

[1.008, 1.037]

The point is that this interval is NOT AROUND ONE.
It does not prove anything but it is CONSISTENT with some positive overall curvature and with spatial closure. So that is a possibility which it is "good science" (to use your expression) to keep in mind.

 

[marcus]

To remind readers, one bit of news from WMAP3 data was that when w (DE EOS) and curvature were simult. constrained by the data you got a 68% conf. interval for Omega that NO LONGER STRADDLED ONE.

The interval for Omega referred to is [1.008, 1.037]
Discussed in Spergel et al Fig 17 page 53. So the centipede upstairs is getting ready for bed and we heard a shoe drop.

We listen for other shoes. Will the scientific community gradually change the nuances in how it talks about this. If Omega REALLY WERE like 1.01 that would be consistent with a spatial finite universe, that is with SPATIAL CLOSURE. Like a big 3-sphere instead of infinite flat euclid 3-space.

OK, this thread is for listening for shoes drop. Don't be in a hurry, just wait. here is a little bump. what does it mean, if anything?

http://arxiv.org/abs/astro-ph/0604335
Cosmological parameters from combining the Lyman-alpha forest with CMB, galaxy clustering and SN constraints
Uros Seljak, Anze Slosar, Patrick McDonald
11 pages, 4 figures

"We combine the Ly-alpha forest power spectrum (LYA) from the Sloan Digital Sky Survey (SDSS) and high resolution spectra with the cosmic microwave background (CMB) including 3-year WMAP, supernovae (SN) and galaxy clustering constraints to derive new constraints on cosmological parameters. The existing LYA power spectrum analysis is supplemented by constraints on the mean flux decrement derived using a principal component analysis for quasar continua, which improves the LYA constraints on the linear power. The joint analysis reduces the errors on all parameters and prefers the simplest 6 parameter cosmological model. We find some tension between the WMAP3 and LYA power spectrum amplitudes, at the ~2 sigma level, which is partially alleviated by the inclusion of other observations: we find sigma_8=0.85+-0.02 compared to sigma_8=0.80+-0.03 without LYA. For the slope we find n_s=0.965+-0.012. We find no evidence for running of the spectral index, dn/dln k=-0.020+-0.012, in agreement with inflation. The limits on the sum of neutrino masses are significantly improved: sum(m_nu)<0.17 eV at 95% (<0.32 eV at 99.9%). This result, when combined with atmospheric and solar neutrino mixing constraints, requires that the neutrino masses cannot be degenerate, m_3/m_1>1.3 (95%). Assuming a thermalized fourth neutrino we find m_s<0.14 eV at 95% c.l. and such neutrino cannot be an explanation for the LSND results. The fit is poor even in the limit of massless sterile neutrino since the constraint on the number of relativistic neutrino species is N_nu=3.19+0.19-0.15 and N_nu>4 is excluded at 99.76%. The constraint on the dark energy equation of state is w=-1.04+-0.06. The constraint on curvature is Omega_k=-0.003+-0.006. Cosmic strings limits are G mu<2.3 10^-7 at 95% c.l."

======================

mean anything? not much I am afraid, more a point for the status quo this time.

It puts Omega in the interval [0.997, 1.009]
which is comfortably consistent with the idea that Omega true value is EXACTLY ONE.

 

[Chronos]

I was reading that same paper today, marcus, and left with the same feeling - wrapped in an old, handmade quilt. WMAP 3 seems to lean in the direction of closure [omega just barely above 1]. Not enough to be compelling, but tantalizingly close. In short, I still think omega is exactly 1.

 

[marcus]

...and left with the same feeling - wrapped in an old, handmade quilt...

can't say anything about Omega at the moment, but quilts are nice arent they. my wife has taken part in several handmade quilt projects---her sister is the real quiltmaker in the family

my favorite thing to read cosmology related papers in is an unbelieveably thick cushy blue terrycloth bathrobe

the centipede upstairs has a lot of shoes left to drop

 

[SpaceTiger]

mean anything? not much I am afraid, more a point for the status quo this time.

It doesn't mean much because it agrees with the standard model? We shouldn't get into the habit of de-emphasizing results simply because they produce no surprises. Remember, the Ly\alpha forest is one of the best cosmological constraints we have and, as they say in the paper,

This is the strongest constraint on the curvature to date and the data continue to show no evidence for it.

 

[Chronos]

I agree with ST, marcus. Observational evidence still overwhelmingly favors the LCDM model. While anomalous observations remain to be explained [e.g., Arpianism], there are not enough to 'throw out the baby with the bath water'.

 

[marcus]

...

the centipede upstairs has a lot of shoes left to drop

here's another

http://arxiv.org/abs/astro-ph/0604616
Extending the WMAP Bound on the Size of the Universe
Joey Shapiro Key, Neil J. Cornish, David N. Spergel, Glenn D. Starkman
9 pages, 16 figures

"Clues to the shape of our Universe can be found by searching the CMB for matching circles of temperature patterns. A full sky search of the CMB, mapped extremely accurately by NASA's WMAP satellite, returned no detection of such matching circles and placed a lower bound on the size of the Universe at 24 Gpc. This lower bound can be extended by optimally filtering the WMAP power spectrum. More stringent bounds can be placed on specific candidate topologies by using a a combination statistic. We use optimal filtering and the combination statistic to rule out the infamous "soccer ball universe'' model."I still claim that the results so far don't mean very much in the sense that I plan to wait for a good deal more reaction. these links are not intended to prove anything either way. they are sampling the MWAP3 fallout.

Niel Cornish is an amusing guy. I remember 3 years or so back his paper about how the U has to be "at least this big". He had a pet monkey that appeared sitting on Cornish shoulder in a picture at his website (Cornish site, not the monkeys)

Make whatever conclusion you want. I'm just collecting some post WMAP3 papers related to the issue of Universe closure or non-closure.

==========================
for the curious, some samples from this particular dropped shoe:"...The WMAP data point to a universe with a total energy density within 2% of critical[3]. This means that even if space is not quite flat, the radius of curvature of the Universe is at least of order the size of the observable Universe, and space can be considered to be nearly flat. ..."

can be considered, I may add, to be FINITE and nearly flat------if one cares to so consider it

I don't particularly like the models with complicated topology such as the DODECAHEDRON thing. So I am glad to see them ruling it more and more out

"XI. CONCLUSION The claim that the topology of our Universe had been found to be that of the Poincaré dodecahedron does not stand up under scrutiny. The signature found in Ref. [8] disappears when one uses the proper S statistic and considers the false positive threshold. While the shape of our Universe remains a mystery, the matching circles test can be used to place a lower bound on the size of the Universe. The previous limit of 24 Gpc [4] can be extended by about 10% using filtering of the WMAP power spectrum. A full search with optimal filtering is now underway. "

more power to you, guys. So roughly speaking the U is sure to be at least some 30 billion parsecs across. Roughly 100 billion light years.

you know that you can find two points that far apart

and hey, it might be flat-out infinite too. we still don't know
in my unauthoritative opinion.

 

[SpaceTiger]

It was an interesting result after the first release, but this release just gives a 10% increase on the topology scale limit. Meh, I guess somebody had to check.

Note that this method more directly addresses the finiteness question than a measurement of the curvature. If the cosmological principle breaks down at large scales, the universe can have any curvature and still be finite. However, I think the detection of circles on the sky would definitively rule out an infinite universe.

 

[marcus]

... However, I think the detection of circles on the sky definitively rules out an infinite universe.

I agree. Thanks for the comment. As you say, circles would rule out infinite, and AFAIK they have not been seen.
(my gut reaction to circles is horror. I hope they are never observed. Rather see simple vanilla infinite than some periodic structure. but decency forbids dwelling on one's prejudices)

 

[Chronos]

I think we can safely rule out 'circles in the sky'. And I share your discomfort with that concept. But, I'm not convinced it rules out a finite, unbounded universe. My concern centers around the argument the universe very much appears to be temporally finite. Hence, I am forced to reject any argument it [the observable universe] is spacially infinite.

 

[marcus]

BTW Ned (SpaceTiger) is coming out very well as a guesser that the community would NOT show signs of shifting off the flat assumption any time soon. If that was his guess.

My guess was different and would have been that by now i would have heard more about it. And I havent. But I expect to just have to wait longer than I at first expected, and am not discouraged.

Today, another paper

Look at Figure 2, on page 4

Shows a 68 % confidence region for Omega_matter and Omega_Lambda where sure enough the {Omega_total = 1} line DOES pass thru, but rather off to one side. So sure enough the data is CONSISTENT with the convenient usual assumption of Omega_total = 1, that is "flat".

And in their verbal treatment the "flat" case is the only one they appear to consider.

And a casual glance at Figure 2 shows that the "SWEET SPOT" of their 68% gaussian oval has about Omega_total = 1.1 roughly.

which as usual if we took it seriously would say "positive curved spatially closed" but which as usual we do not take seriously but attribute to mere vagary of the data.

the funny thing is it seems to happen all the time.The Hubble diagram extended to z>>1: the gamma-ray properties of GRBs confirm the Lambda-CDM model
C. Firmani (1,2), V. Avila-Reese (2), G. Ghisellini (1), G. Ghirlanda (1) ((1) Osserv. Astron. di Brera, Italy; (2) Instituto de Astronomia, U.N.A.M., Mexico)
5 pages, 4 figures included. Submitted to MNRAS Letters

"Tight constraints on cosmological parameters can be obtained with standard candles spanning a range of redshifts as large as possible. We propose to treat SN Ia and long Gamma-Ray Bursts (GRBs) as a single class of candles. Taking advantage of the recent release of the Supernova Legacy Survey and {\it the recent finding of a tight correlation among the energetics and other prompt gamma-ray emission properties of GRBs}, we are able to standardize the luminosities/energetics of both classes of objects. In this way we can jointly use GRB and SNIa as cosmological probes to constrain Omega_m and Omega_L and the Dark Energy equation of state parameters through the same Bayesian method that we have, so far, applied to GRBs alone. Despite the large disparity in number (115 SNIa versus 19 GRBs) we show that the constraints on Omega_m and Omega_L are greatly improved by the inclusion of GRBs. More importantly, the result of the combined sample is in excellent agreement with the Lambda-CDM concordance cosmological model and does not require an evolving equation of state for the Dark Energy."

As you recall in the WMAP3 report there was that figure with 68% confidence interval Omega_total being
[1.008, 1.037], not even around one! This is much broader and less precise, but it is around one (just a bit off to the upside)

 

[Garth]

BTW Ned (SpaceTiger) is coming out very well as a guesser that the community would NOT show signs of shifting off the flat assumption any time soon.

Is that flat or conformally flat?

Today, another paper

Look at Figure 2, on page 4

Shows a 68 % confidence region for Omega_matter and Omega_Lambda where sure enough the {Omega_total = 1} line DOES pass thru, but rather off to one side. So sure enough the data is CONSISTENT with the convenient usual assumption of Omega_total = 1, that is "flat".

(emphasis mine)

Note, it is actually the other way round - deductions from the data of standard candles and rulers, as well as CMB anisotropies, are dependent on the spatial geometry of the universe.

These data sets are indeed observed to be consistent with a spatially 'flat' geometry and it is this 'flatness' that requires \Omega_{total} = 1. However, THAT deduction leads to the invocation of problematic DE.

Conformally flat geometries are also consistent with these data sets, but they do not require \Omega_{total} = 1, and so DE may not exist after all.

Note further, the linearly expanding universe is also consistent with the distant S/N Ia data, however, such a conformally flat geometry and linearly expanding scale factor would require a modification of GR.

Garth

 

[Chronos]

If we leave out the alleged CMB anisotro[cow]pies, the puzzle box is not that difficult to solve.

 

[Garth]

If we leave out the alleged CMB anisotro[cow]pies, the puzzle box is not that difficult to solve.

Well, the puzzle box now includes problematic DE, exotic non-baryonic DM, Higgs bosons/inflatons, (all as yet undiscovered in laboratory physics), a possible age problem in the early universe, as well as a Pioneer anomaly, and the alleged axis of evil and deficient quadrupoles.


Agreed, those puzzles may be solvable, nevertheless, it is important to keep viable options open, we may never know what may lay round the next corner!

Garth

 

[selfAdjoint]

Well, the puzzle box now includes problematic DE, exotic non-baryonic DM, Higgs bosons/inflatons, (all as yet undiscovered in laboratory physics), a possible age problem in the early universe, as well as a Pioneer anomaly, and the alleged axis of evil and deficient quadrupoles.


Agreed, those puzzles may be solvable, nevertheless, it is important to keep viable options open, we may never know what may lay round the next corner!

Garth

Bolded matter is a bit of a stretch for cosmology? Why not include the non-mating of quantum and GR then, or just the whole world of things unknown in all of physics?

 

[Garth]

Bolded matter is a bit of a stretch for cosmology? Why not include the non-mating of quantum and GR then, or just the whole world of things unknown in all of physics?

Indeed, why not include the QM/GR interface in the puzzle box?

Modern cosmology is founded on both.

As I said, just as well to keep all viable options open.

Garth

 

[SpaceTiger]

BTW Ned (SpaceTiger)

My name is Nick.

...is coming out very well as a guesser that the community would NOT show signs of shifting off the flat assumption any time soon. If that was his guess.

It wasn't exactly a "guess", I work with the people doing the experiment. The issue is not one of physical interpretation, just of interpretation of quoted errors. The community has no particular reason to question the WMAP team's interpretation of their own errors. The only way you could see a change of the community's view of "flatness" is if somebody incorporated more data or the error analysis was shown to be flawed.

And a casual glance at Figure 2 shows that the "SWEET SPOT" of their 68% gaussian oval has about Omega_total = 1.1 roughly.

which as usual if we took it seriously would say "positive curved spatially closed" but which as usual we do not take seriously but attribute to mere vagary of the data.

You're talking about a data set that only constrains \Omega_k to ~20% and which includes unity in what appears to be a <50% confidence interval. By contrast, the precision of WMAP is of order a percent or two. You'd need ~100 such independent results with minimal systematics to even begin to compare to WMAP's constraint on flatness.

the funny thing is it seems to happen all the time.

Not in my experience. When WMAP was included with other data sets (such as SDSS), the vast majority of them brought the estimate on \Omega_k down.

 

[marcus]

My name is Nick.
...

Of course Nick Bond! Just carelessness, sorry.

thanks for jogging my memory, which needs it sometimes. I just saw a list of your papers on arxiv
http://arxiv.org/find/grp_physics/1/au:+bond_N/0/1/0/all/0/1

Impressive! congratulations!

the search turned up 9 papers. I remember you saying you were in the PhD program at Princeton. You must be nearly done, finishing up thesis and so on.

Not in my experience...

You have such different experience of this from me, which makes life interesting.
My experience is that for some years now whenever I see ANY estimate of Omega_total it is NEVER on the downside of one.

whatever the dataset or the way it is measured it is always plain 1, or the confidence interval is LOPSIDED towards the upside (but still includes 1). Or else as in that WMAP3 case which we discussed, the confidence interval is ENTIRELY on the upside of 1 and doesn't even include 1.

One certainly doesn't want to over-interpret the data! (Seriously, no joke!) One wants to be very sober and judicious about this and refrain from attributing undue significance!

But my nagging experience is that the published confidence intervals always come out a bit upside, and never downside.

I assume that you, Garth, Chronos and so on HAVE seen confidence intervals that are lopsided downwards. Indeed one may INFER the existence of datasets that do make for such (like Sloan Digital Sky Survey) because MIXING SDSS data with WMAP3 data brings Omega down! I have seen a bunch of mixed data results tabulated in Spergel et al. As you indicate. But that is inference. the fact is, I have not seen anybody make a confidence interval (recently at least) that is on downside of one.

Maybe someone wants to supply a link?

It is curious that your experience is different.
=====================
I think we have already been through much of this discussion and there is no need to repeat.

But if you do happen to have a link to some recent published estimate of Omega that has a confidence interval downwards of one (in contrast to what I have seen), that would be something NEW for me and I would be very glad to see it.

Please give a page reference with the link. This is something that may have been staring at me all the time and my sometimes overworked eyes did not spot!

 

[SpaceTiger]

Maybe someone wants to supply a link?

The 2dF measurements of large scale structure yield an estimate of curvature that is not only low, but almost two-sigma below flat at a precision of ~5%:

http://lanl.arxiv.org/abs/astro-ph/0507583"

Refer to Table 2.

You have such different experience of this from me, which makes life interesting.
My experience is that for some years now whenever I see ANY estimate of Omega_total it is NEVER on the downside of one.

This should suggest to you that something's wrong. To see what I mean, let's just suppose for the moment that you're right about the curvature being positive and let's take the upper WMAP error bar -- \Omega_{tot} = 1.038. Now let's ask the question, if perform an experiment with gaussian random errors on this parameter of order 20% (as in the paper you just quoted), what fraction of the time will I measure \Omega_{tot}&gt;1? The answer is about 57.5% of the time. That means that, even in the upper range of curvature suggested by WMAP, you should still see such measures give \Omega_{tot}&lt;1 in 42.5% of data sets. The fact that you never see such things suggests one or more of the following:

1) Your sample is too small to be meaningful.
2) Your sample is heavily biased.
3) The measurements you're thinking of are not all independent.
4) The experiments you're thinking of suffer from systematics that always bias them greater than one.
5) The experiments have overestimated their error bars.

The last two things seem pretty unlikely to me, so you should probably consider looking into the first three.

 

[marcus]

The 2dF measurements of large scale structure yield an estimate of curvature that is not only low, but almost two-sigma below flat at a precision of ~5%:

http://lanl.arxiv.org/abs/astro-ph/0507583"

Refer to Table 2.


...
3) The measurements you're thinking of are not all independent.
...

this is an excellent one to add to the collection, thanks. It is from July 2005, so fairly recent though not the most so. Let's see what it says.
I am looking at Table 2, as you suggest. don't have time to study it at length but here's what I see it say:

the Omega_k error bar is around ?0.074 with limits +0.049 and -0.052

so as I read it the error bar is between [-0.126, -0.025]

this is reminiscent of my positive curvature benchmark Spergel et al

folks will recall Figure 17 on page 55 of the famous WMAP3 report by Spergel et al "implications for cosmology" where they gave a 68 % confidence interval for Omega_k which was
" ?0.024 +0.016 ?0.013 at the 68% confidence level."

this translates into [-0.037, -0.008]

that Spergel et al interval meant that we had Omega in the range
[1.008, 1.037]

that is the curious upside picture I see a lot of

OF COURSE THESE CONFIDENCE INTERVALS PEOPLE PUBLISH ARE NOT SEPARATE INDEPENDENT MEASUREMENTS, I am not doing statistics with them , THEY ARE ALL BASED ON THE SAME FEW DATASETS, like SDSS and WMAP which gradually get improved and people keep re-using.

I just so far didnt see confidence intervals favoring the downside. Not really surprising either. And I am curious did anybody else?

===============

Nick thanks so much for the new paper! I will add it gratefully to my collection.

As far as I am concerned we are not arguing and this is partly repetitious. But here you have given me something new and I am glad!

Please explain it to me and interpret, if you so desire.

 

[marcus]

this is an excellent one to add to the collection, thanks. It is from July 2005, so fairly recent though not the most so. Let's see what it says.
I am looking at Table 2, as you suggest. don't have time to study it at length but here's what I see it say:

the Omega_k error bar is around -0.074 with limits +0.049 and -0.052

so as I read it the error bar is between [-0.126, -0.025]

..

The nice paper Nick kindly provided is this one first posted July 2005

http://lanl.arxiv.org/abs/astro-ph/0507583
Cosmological parameters from CMB measurements and the final 2dFGRS power spectrum
Ariel G. Sanchez (Cordoba), C. M. Baugh (Durham), W. J. Percival (Edinburgh), J. A. Peacock (Edinburgh), N. D. Padilla (Catolica), S. Cole (Durham), C. S.Frenk (Durham), P. Norberg (ETH, Zurich)

MNRAS, in press. Minor revision after referee's report. 22 pages, 18 plots. Colour figures for talks (including additional plots which do not appear in the paper) can be downloaded from this http URL
Monthly Notices of the Roy.Astron.Soc. 366 (2006) 189-207

From Table 2 of this paper one gets a confidence interval for Omega_k
of [-0.126, -0.025]

this is the same all-negative interval situation that was so remarkable in Spergel at al, and seems to be yet another case of positive curvature---that is of Omega being on the upside of 1.

If one treats this Table 2 estimate the same way one treated Spergel, one gets this for Omega_total
[1.025, 1.126]

that is a little more marked than the Spergel WMAP3 thing of
[1.008, 1.037]

So far I don't see how this contradicts my general impression of how the papers keep leaning towards positive largescale curvature. I could very likely be missing something. Dont have time to study the whole paper and these damned minus signs and double negatives keep buzzing around like flies.

But anyway, I treat it exactly like I did Spergel et al, praying that they are using the same notation, and that's how it comes out.