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

[kmarinas86]

I'm not sure what you mean by "this" that is true.

"this" refers to the new WMAP data, which suggests a possibility of a closed universe.

 

[marcus]

"this" refers to the new WMAP data, which suggests a possibility of a closed universe.

well it certainly suggests the possibility!

but they say their data is "consistent" with several interpretations that they mention

this is usual with academic writing, so there is not one simple message that you can say if this is true then so and so.

but I certainly agree with the general idea of what you say.
============================
BTW kmarinas, there is some good reference material on these matters
look at post #2 of the Astronomy Reference sticky thread

https://www.physicsforums.com/showthread.php?p=136400#post136400

A very good article that you see a link to there is

Charles Lineweaver
Inflation and the Cosmic Microwave Background

I posted that a couple of years ago because I found that article really really useful.

It addresses some of the issues you raised. (how accelerating expansion changes the picture from what was commonly thought pre-1998)

It also addresses something Space Tiger mentioned. One of the reasons that inflation was invented----or that people found the idea so attractive once it had been invented----is that it solved the "flatness problem".

Lineweaver talks about that IIRC. You might want to check it out. It is very readable.

there is a lot to learn in connection with this bunch of ideas (the possible spatial non-flatness of the universe----how inflation can have stretched a curved space out to be so very nearly (but not perfectly) flat. and so on.

 

[Chronos]

The more important result, IMO, is 'mainstream' cosmology appears to have survived intact [and am tempted to say 'I told you so' to a few souls]. I'm intrigued that the WMAP team included Y3 results. I think it's also safe to say a huge storm of controversy is brewing. There is an incredible amount of data presented in this release and it will take years to sort out the implications. One thing that impresses me is the WMAP team went to great lengths to detail the assumptions used. I predict that will prove to be an invaluable resource for future researchers. All in all, I would say they have done a splendid job.

 

[SpaceTiger]

Good, then there is no reason to argue is there?

...

What I am interested in emphasizing is the POSSIBILITY (among others) that the universe is spatially finite with a very small positive curvature.

If that's all you're interested in, then I have no argument. In fact, I'll go one further -- any measurement of the curvature of the universe that is consistent with flatness is also consistent with a small positive or negative curvature. This follows trivially from the fact that no measurement has infinitely small error bars.

When I said you were reading too much into their words, I meant that they did not choose those words to imply anything special, they were just stating the results as they were. What confuses me is why you think this is such an interesting topic of discussion as concerns the WMAP data. It has always been possible that the universe is barely closed or barely open -- WMAP has changed nothing in that arena. Also, your concerns about a finite or infinite universe will not be resolved by the measurement of the curvature because the universe can have a non-trivial topological structure (which locally appears to be open, closed, or flat).

 

[marcus]

If that's all you're interested in, then I have no argument. In fact, I'll go one further -- any measurement of the curvature of the universe that is consistent with flatness is also consistent with a small positive or negative curvature. This follows trivially from the fact that no measurement has infinitely small error bars.

When I said you were reading too much into their words, I meant that they did not choose those words to imply anything special, they were just stating the results as they were. What confuses me is why you think this is such an interesting topic of discussion as concerns the WMAP data. It has always been possible that the universe is barely closed or barely open -- WMAP has changed nothing in that arena. Also, your concerns about a finite or infinite universe will not be resolved by the measurement of the curvature because the universe can have a non-trivial topological structure (which locally appears to be open, closed, or flat).

We seem to be closer to agreement now
I am glad. I do not like to argue nor am I good at it. I am not "reading in" to what Spergel et al say. I just quote them and point out what they actually said. I don't pretend to be able to get inside their heads and tell WHY they said this or that. Objectively they left open a possible interpretation. And as I think you now realize, I am not "over-interpreting the data". I quote Spergel et al's interpretation----as in figure 17 on page 50 of the arXiv preprint.

I am interested in the possibility that the universe is finite. I want to consider that possibility. You seem ready to allow me to do that in a friendly spirit. You say:

If that's all you're interested in, then I have no argument.

Again I must say I am very glad for this.

BTW You express incomprehension that I should be interested in considering this possibility (a finite universe with slight positive curvature) and gauging the consistency of that with WMAP results. That is OK, we don't have to understand each others motives.

It gets boring having to JUSTIFY being interested in something.

I may be the only one here at PF at the moment who is interested in the fact that a finite universe is consistent with the WMAP results (as one possibility) and who wants to think about that. If that is so, that's OK too. Let me get on with it. Maybe some other people will get interested later.

 

[marcus]

To pick up where we left off, here is what I was saying in post #31.
Please anybody who wants to discuss these things, download the most recent version. The one posted yesterday on arXiv

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

This version is the one for publication in ApJ and is slightly different from the one at the NASA site that I gave a link to a few days ago.
The main reason to all use the same version is the pagination. The key figure 17 in the "non-flat" section of the paper is on page 50 in the arXiv version, and on page 43 in the earlier version---for example.

I guess this arxiv preprint is pretty much the finished paper as it will appear in ApJ. Let us look at the conclusions on page 70

Here is the second of three conclusions, at the end of the paper:

"The WMAP data are consistent with a nearly flat universe in which the dark energy has an equation of state close to that of a cosmological constant, w = -1. The combination of WMAP data with measurements of the Hubble Constant, baryon oscillations, supernova data and large-scale structure observations all reinforces the evidence for dark energy."

I have highlighted "nearly flat" because it allows for the possibility that Omega is slightly larger than 1 and therefore is consistent with the idea of a spatially finite universe with a slight positive curvature.

the authors of the paper MIGHT have said flatly that
"The WMAP data are consistent with a flat universe." period.
but as it happens they did not say this---they left open another possibility to be considered.

I stress that I am not guessing about what they did or did not have in mind. Objectively this is what they said. Academics are usually rather careful in their wording especially in the final paragraphs of the "conclusions" at the end of a major paper. I know nothing about their intent, but intentionally or not they left open a certain possibility which I want to consider carefully.

the first question I want to think about is WHAT SORT OF OBSERVATIONAL EVIDENCE MIGHT in future SUPPORT THE NON-FLAT UNIVERSE model and might help to RESOLVE THE FINITENESS ISSUE.

As a rule in science questions are never 100 percent resolved. there are always error bars. If you get 68% someone can always ask for 95% and if you get 95% someone can ask for 98%. But people do have a sense of what is reasonable and the consensus on issues can gradually shift.

 

[marcus]

...the first question I want to think about is WHAT SORT OF OBSERVATIONAL EVIDENCE MIGHT in future SUPPORT THE NON-FLAT UNIVERSE...

I am going to take my time answer this. Maybe say some more later today. But first here is something very obvious.
If you are looking for evidence for non-flat, then you want to see error bars for Omega that DO NOT INCLUDE ONE.

The first year WMAP results, if I remember correctly, had the confidence interval 1.02 +/- 0.02
or in other words [1.00, 1.04]. That was not very satisfactory.

It was inconclusive for a couple of reasons. for one thing, the flat case, Omega = 1, is still just barely in this interval. The flat case is not excluded from the interval. Also there is only a couple of digits accuracy, which is not very much.

In the three-year WMAP results there are several implied confidence intervals for Omega (I mean of course total Omega, Omega_tot, if I want to write one of the components I will use a subscript).

Several intervals are given depending on whether it is WMAP data alone, or combined with other batches of data (like Sloan Digital Sky Survey SDSS, or the supernova data). And depending on what things are being allowed to vary so we can see how they are constrained by data.

An illustrative example, from the paper we are considering, is the figure 17 on page 50 that I mentioned.

this is with COMBINED data (WMAP, SDSS, supernova, 2dFGRS) and it is where you let both w and Omega vary, since neither are known and they influence each other, and try to estimate ("constrain") both numbers SIMULTANEOUSLY.

In my view it is an impressive achievement that the Y3 data is so good that it allows one to simultaneously constrain both these things. That is why figure 17 is one of the most impressive results in the whole paper, in my opinion. In the past one would have felt obliged to PEG a value for w in order to estimate Omega----the data wasnt good enough to constrain both very effectively so you had to make an assumption about one in order to estimate the other.

Anyway the upshot is when you do all that you get, in that figure 17 case, a 68 percent confidence interval for Omega that is

[1.008, 1.037]

Notice that the FLAT CASE IS EXCLUDED FROM THIS INTERVAL. Something new. Now very obviously that is not the end of the story
That is just the beginning. 68% is not 95%, for one thing. There are more CMB missions planned.

But it illustrates how things might look some time in future and one could ask WOULD THIS TEND TO SHIFT THE mainstream CONSENSUS?

We are talking about how some of the issues might be resolved. Suppose in future some CMB mission publishes a 95% confidence interval [1.008, 1.037] for Omega.

For sake of illustration, the same interval just that it is 95% instead of 68%. Suppose.

The point is that the exact flat case of Omega = 1 exactly IS NOT IN THIS INTERVAL.

What I am talking about is an ASYMMETRY in the logic. You can never exclude the finite non-flat case if you keep getting narrower intervals but they are all around 1. Even if you narrow it down to [0.999, 1.001]
there is still the possibility that it is 1.0001 and positive curved and finite.

In case the true Omega is exactly 1, the data will always be consistent with slightly non-flat finite. Even if the interval is [0.9999, 1.0001]

But if true Omega is, say, 1.01, then you CAN hope to exclude the exactly 1 perfectly flat case. In fact an interval like [1.008, 1.037] would support that conclusion, if it were very high confidence.
Nothing in science is ever 100% certain but such a result would be very supportive and would undoubtably influence the mainstream consensus.

Of course we don't yet have a high confidence interval, we only have the 68 percent that you see in figure 17, and things like that.

There are also OTHER OBJECTIONS which I want to discuss later. Like suppose the universe really is perfectly flat if you go out way beyond the observable portion of it
this is the kind of thing people speculate about---it shades off into eternal inflation and multiverses and landscape and with some people it may shade off into a kind of fantasy world.

But let's not go that far. Let's just imagine that the really large scale universe is Omega =1 but the part we can see turns out to be very slightly positive curved. OK that picture would allow people who are attached to the infinite universe idea to keep their infinitude while accepting Omega > 1.

Lot of things to think about here. Plenty of possibilities to consider.

what I am expecting is that there will be a barely perceptible shift in nuance in how mainstream cosmologists talk, as they assimilate the Y3 data. I have always taken my cues from mainstream consensus people---like Charles Lineweaver and Michael Turner---over the past several years. So I want to keep alert to gradual shifts in how they (and people like them) look at things.

Occam's razor is likely going to play a role, at least for some people. If it turns out that Omega is slightly greater than one with HIGH confidence (which we don't know yet) then one SIMPLE way to interpret that is that the universe IS ACTUALLY THE WAY IT LOOKS and does have a slight positive curvature.
And then that will take some explaining, for sure! So my personal opinion is the story here is just getting started and nobody can say how the issues will resolve.

 

[Chronos]

I'm sympathetic, but reluctant to commit just yet marcus. A more significant issue in my mind is the value derived for w. The departure from the dark energy equation of state [w = -1] is more troublesome to me than Omega-m in making the flatness case.

 

[marcus]

I'm sympathetic, but reluctant to commit just yet marcus. A more significant issue in my mind is the value derived for w. The departure from the dark energy equation of state [w = -1] is more troublesome to me than Omega-m in making the flatness case.

Hi Chronos, I can understand. Actually there is no reason we always have to focus on figure 17. That is merely one possible way to analyze the data---one take on it. Pegging w = -1, which we would both be more comfortable with (!), seems to give qualitatively much the same result about Omega.

but if we do focus on figure 17, what you see is a 68 % confidence interval for w which is CONSISTENT with assuming w = -1 exactly. That is the interval is -1.062 (+ 0.128 or -0.079) that is

[-1.141, -0.934]

and -1 is IN that range. So that is just what one would expect to see in the case that w= -1 exactly. Which is the nice case where dark energy is just the cosmological constant that Einstein put in his equation. A comfortable old familiar mystery, not some scary new quintessence threatening to do a big rip on us.

One thing that makes me so happy with Y3 is that the data are good enough to constrain both these things at once. As I said earlier that is an impressive sign of high quality data---at least it impresses me. And AFAIK it is new. I didnt see that earlier before Y3. One of the little perks of being around at this stage in the game.

 

[wolram]

I am sorry Marcus, but i have to ask how these numbers influence the
(big picture), it may be that they stand the test of time, but then the picture could change, future observations may refine them in some way up or down, and this is only one in many (derived) figures, i only say (derived) as
i have no knowledge of any fixed constants, it seems to my small brain that the juggling of many inputs can still give many outputs, i do dearly want some (big picture) and can guess your ansewer, but where are you going ?

 

[SpaceTiger]

I'm prone to agree with Chronos on this one. Looking at WMAP results alone, one might be inclined to think that there is more reason to doubt the standard model's value of the curvature, but you can see very clearly that when other experiments are included, the value is almost always pulled down toward zero. This is what one would expect from a flat universe at this precision.

Dark energy, however, has been getting conflicting results in the astronomical community and the underlying theory is extremely shaky. We don't really understand where a cosmological constant would come from. WMAP fits assume a simple constant w model, 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.

 

[marcus]

I am sorry Marcus, but i have to ask how these numbers influence the
(big picture), ...where are you going ?

One of the rules of the game is that you shouldn't speculate too far ahead.
When good scientists publish error bars, the hope is that future data will only narrow things down within those error bars, not jump out. And thankfully a lot of the time this is how it happens.

I see Nick (SpaceTiger) has kindly joined in the discussion. I will withhold comment in case he wants to respond to your question.

Notice that Chronos has said that he thinks it is more interesting (or "troublesome") that w is being estimated at something less than -1 (plus or minus). That is, dark energy might not simply be the Einstein equation's cosm. const. And Nick appears to agree that this is an interesting possbiliity.

I can't give you a satisfactory answer Wolram. Keep listening. maybe someone will hazard a guess.

 

[wolram]

Thank you Marcus, i wish we could consentrate on this one (enigma) do it to
death, sorry ST, Chronos, but in my mind it will not go away, is the obervational evidence a good clue? is the maths leading to a solution?

 

[SpaceTiger]

I am sorry Marcus, but i have to ask how these numbers influence the (big picture)

With this analysis alone, the big result is the continuing consistency of the standard model, including evidence for inflation. These results don't say anything interesting about the possibility of a non-flat universe or a non-cosmological constant, but the data will continue to be analyzed and who knows, maybe something else will turn up.

The measurement of the slope of the spectrum of perturbations (n_s) is consistent with the prediction for inflation, but the real smoking gun would be a detection of B mode polarization from gravitational waves at the surface of last scattering. WMAP doesn't have the precision to make this measurement and it's likely that we'll have to wait as much as 10 or 20 years before we see an experiment capable of reaching the level where we expect to see it.

Since WMAP is primarily probing an era when the dark energy density was small relative to matter and radiation (z~1100), it doesn't tell us very much about w. When combined with other data sets, we can improve the error bars, but much of the community would like to see an experiment dedicated to measuring w and its time derivatives. It's yet to be seen whether or not this will be realized, but there are still measurements we can do from the ground (including gravitational lensing measurements) that will improve the constraint.

The measurement of the optical depth to the surface of last scattering tells us about when the universe was reionized, which in turn tells us about when the first stars were formed. The first release had a very sketchy analysis (and subsequent) measurement of the optical depth that indicated starbirth at z~17. Improved analysis of the polarization data has brought this down to z~11. Although this gives us less time to form high-z objects (like supermassive black holes and massive galaxies), it's more consistent with the measurements of reionization from SDSS quasars, which indicate a non-negligible neutral fraction at z~6.

The WMAP data, taken alone, are leaning in the direction of a slightly closed universe, but this should be taken with a grain of salt, since other measurements tend to pull things in the other direction. I disagree with marcus that there is something interesting to be taken from that, but I certainly won't rule out the possibility that the universe is closed at this level. We shouldn't take the confidence intervals too literally, since the analysis is complex, the parameters are highly degenerate, and the systematics are not fully understood. I don't think the WMAP team would tell you that they're 68% confident the values lie within their one-sigma error bars, especially given that they often quote multiple figures (which depend on the model assumptions).

I may be forgetting something, but that's a brief review of the main results for the big picture of cosmology. Is there anything in particular you're interested in?

 

[SpaceTiger]

Thank you Marcus, i wish we could consentrate on this one (enigma) do it to
death, sorry ST, Chronos, but in my mind it will not go away, is the obervational evidence a good clue? is the maths leading to a solution?

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.

 

[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