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

[marcus]

Peter Woit called attention to the liklihood that new WMAP data will be coming out soon

for some additional detail here is a post from Anthony Lewis (Cambridge)

http://cosmocoffee.info/viewtopic.php?p=1391#1391He says that around 23 March there will be one or more conference talks about the Three Year WMAP data. Spergel is one of the principals in WMAP and he is scheduled to give a talk

D. N. Spergel et al. "Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Cosmology"

so presumably the data will have to be released by that time.

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

the last big batch of CMB cosmology data was Bennett et al (2003).

It has been a long time and some people seem to be quite impatient.

The parameter people seem most interested in is Omega and the Bennett 2003 estimate was 1.02 +/- 0.02
this includes the spatially flat case (exactly 1) and also includes the case where space has a slight positive curvature and is presumably finite. (although time is not bounded)

If they could reduce the error-bar and keep the same 1.02, it would send out philosophical shockwaves. For instance if the new data said that Omega is 1.02 +/- 0.01
then it would send out the notion that the universe is not spatially flat but is very slightly positive curved, and that it is spatially finite
and that it will nevertheless keep expanding (at an accelerating rate).

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

I can't guess anything about the new data, but different results could have impact on people's picture of the universe, and also remember the new data could be exactly the same as the old data and there could be no interesing change too. But the possibilities are just interesting enough so one should keep alert to the forthcoming batch of new data on the CMB

=================
to check out the old data
http://map.gsfc.nasa.gov/m_mm/mr_wmapdata.html

http://map.gsfc.nasa.gov/m_mm/pub_papers/firstyear.html

here is a good one:
http://lambda.gsfc.nasa.gov/

even better:
http://lambda.gsfc.nasa.gov/product/map/current/

their summary of cosmological parameters
http://lambda.gsfc.nasa.gov/product/map/current/wmap_parameters.cfm

 

[Garth]

Peter Woit called attention to the liklihood that new WMAP data will be coming out soon

to be precise here is a post from Anthony Lewis (Cambridge)

http://cosmocoffee.info/viewtopic.php?p=1391#1391


He says that around 20-22 March there will be one or more conference talks about the Three Year WMAP data. Spergel is one of the principals in WMAP and he is scheduled to give a talk

20-22 March 2006 or 2007?

Pardon by scepticism! We've been waiting a long time.

Garth

 

[EL]

20-22 March 2006 or 2007?

Pardon by scepticism! We've been waiting a long time.

Heard something about that if they don't present any data within the next few months they will have a hard time getting any more funding, so probably they will present at least a piece of it very soon...

 

[SpaceTiger]

Yeah, I'm pretty sure the big one is coming. According to David Spergel, some of the papers have been submitted to NASA and the release is now up to them.

 

[marcus]

20-22 March 2006 or 2007?

Pardon by scepticism! We've been waiting a long time.

Garth

yes I know we've been waiting a long time

I meant March 2006, in other words in the next week or so
but your skepticism is understandable

 

[wolram]

Yeah, I'm pretty sure the big one is coming. According to David Spergel, some of the papers have been submitted to NASA and the release is now up to them.

Why, NASA and not the virgin results ?

 

[SpaceTiger]

NASA just announced that the WMAP results will be released this Thursday. You will be able to get the papers and press releases from:

http://lambda.gsfc.nasa.gov/

 

[SpaceTiger]

Why, NASA and not the virgin results ?

I'm sorry, I don't understand your question.

 

[EL]

NASA just announced that the WMAP results will be released this Thursday.

That's some really exciting news!

 

[Garth]

The parameter people seem most interested in is Omega and the Bennett 2003 estimate was 1.02 +/- 0.02
this includes the spatially flat case (exactly 1) and also includes the case where space has a slight positive curvature and is presumably finite. (although time is not bounded)

If they could reduce the error-bar and keep the same 1.02, it would send out philosophical shockwaves. For instance if the new data said that Omega is 1.02 +/- 0.01
then it would send out the notion that the universe is not spatially flat but is very slightly positive curved, and that it is spatially finite
and that it will nevertheless keep expanding (at an accelerating rate).

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

I can't guess anything about the new data, but different results could have impact on people's picture of the universe, and also remember the new data could be exactly the same as the old data and there could be no interesing change too. But the possibilities are just interesting enough so one should keep alert to the forthcoming batch of new data on the CMB

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

That is certainly interesting - it is generally thought that \Omega is just greater than unity already - this release might harden that estimate.

However the most interesting thing for me is whether the quadrupole and other low-l mode deficiencies are confirmed or not and whether an explanation of such a deficiency is offered.

Garth

 

[Chronos]

I anticipate the results will be hugely complicated and inspire much speculation. I would not at all be surprised that it suggests a spatially finitite universe. The existing data already strongly leans that way.

 

[SpaceTiger]

I anticipate the results will be hugely complicated and inspire much speculation. I would not at all be surprised that it suggests a spatially finitite universe. The existing data already strongly leans that way.

There's a talk on the results later today. If I have time tonight, I'll make a summary post in this forum.

 

[marcus]

I just looked at Spergel et al paper
http://lambda.gsfc.nasa.gov/product/map/dr2/pub_papers/threeyear/parameters/wmap_3yr_param.pdfCheck out figure 20 on page 48
and the caption under figure 21 on page 49

To me it now seems more likely the U is spatially positive curved finite

this is my non-expert take on it and I do not see a relevant error-bar
and there is some balancing and guarded-ness in how they discuss it, which is appropriate, but that is how it looks to me at first sight

 

[hellfire]

I took a fast look to the paper and I must say I am a bit disappointed because I was expecting some kind of surprise after the long time we had to wait for these results. I assume that this long time was needed to reach a level of precision on the analysis and conclusions. However, I found not very much information and some vagueness about some issues that I had expected to be treated in detail, such like SZ contamination, ISW and low multipole problem. These are controversial issues that led to alternative models. The paper seams to rely very much on other experiments and it is also repeatedly mentioned the high expectations on future surveys. I assume one has to get used to the fact that current accurate cosmological models are set up like a mosaic, giving us a picture of the whole universe that can be undestood only taking into account all pieces of different precision experiments. This is just my personal opinion after a very fast reading. Let's see what others have to say about it, especially SpaceTiger...

 

[marcus]

question to Space Tiger
there is a parameter Omega-sub-K
which they call "spatial curvature"

I do not see this defined anywhere in terms of other parameters.
Also it is not in the corresponding Spergel et al first-year-data paper

could you please define it for us

==================
what puzzles me is that the old estimate of Omega_total seemed to be saying that the U was mostlikely flat (Omega = 1) or nearly flat with a slight positive spatial curvature (like if Omega = 1.01)

Now they have introduced this Omega_k and estimate that it is around -0.015

it seems to me that a NEGATIVE Omega_k is associated with a slight POSITIVE curvature

if this is true it is confusing

So for instance could it be that they have defined Omega_k as follows:

Omega_k = 1 - Omega_total

?

any clarification? thanks in advance.

 

[hellfire]

Omega_k = 1 - Omega_total

This is right. Take the first Friedmann equation:

H^2 = \frac{8 \pi G}{3c^2} \rho_m - \frac{kc^2}{a^2} + \frac{\Lambda c^2}{3}

divide by H^2 and you will get:

1 = \Omega_m + \Omega_k + \Omega_{\Lambda}

 

[George Jones]

So for instance could it be that they have defined Omega_k as follows:

Omega_k = 1 - Omega_total

?

Yes, this is the curvature "density" - a notational covenience that is often used in cosmology. A c is often used for the subscript k.

Omega_k = - k/(Ha)^2

Regards,
George

 

[marcus]

thanks to you both!

 

[marcus]

OK, thanks for the help. And thanks in advance for help with this!
We are talking about Spergel et al
http://lambda.gsfc.nasa.gov/product/map/current/map_bibliography.cfm
the "implications for cosmology" article that just appeared

a quick link is
http://lambda.gsfc.nasa.gov/product/map/dr2/pub_papers/threeyear/parameters/wmap_3yr_param.pdfPlease look at page 43 figure17and you will see that the 68% confidence interval for Omega_k is

[-0.037, -0.008]

that is what they give when they say -0.024 plus 0.016 or minus 0.013

...[EDIT to be precise, this is when w, the dark energy equation of state, is allowed to vary and be constrained by the data along with curvature]...So by the definition of Omega_k which,e.g. hellfire gave, we have an estimate of Omega_total

[1.008, 1.037]

so at 68 % confidence the universe is not flat.

instead, at that confidence level, it is positive curve spatial finite.

saying this explicitly may bother some people because we are used to making the simple, very practical, assumption of flat infinite and the data is still "CONSISTENT" with that customary simple assumption. that is, it doesn't exactly rule it out

but I would say that even though the data may be consistent with the flat infinite picture many of us are used to, that one should still keep the possibility in mind that we may be moving towards a picture where we assume Omega_total is a wee bit over unity.

 

[SpaceTiger]

So by the definition of Omega_k which,e.g. hellfire gave, we have an estimate of Omega_total

[1.008, 1.037]

so at 68 % confidence the universe is not flat.

instead, at that confidence level, it is positive curve spatial finite.

That's a little deceptive. First of all, the value of the curvature and the error bar are both dependent on which parameters you allow to run free (e.g. we could peg w at -1). It's also dependent on how much information you include. On page 50, table 11 shows the value of \Omega_k one gets after including various other data sets and most of them are consistent with flatness within the 1\sigma error bars.

So I would not say that we're 68% confident the universe is not flat. The data are, of course, consistent with both a closed universe and an open universe as well, but we can't yet distinguish with any confidence. From inflation, we do expect deviations from flatness, but probably not at this level. I think the deviations are expected at the next decimal place.

In interpreting these parameters, it's best to ask whether or not a particular model is consistent with the measurements. The percentage confidence in the value of a particular parameter is model-dependent and depends on error bars that are often crudely approximated. We usually don't take notice of deviations from theory until they're several sigma.

 

[marcus]

Any brief statement is apt to be misleading, so let's try to give a more complete picture. I thought about pegging w = -1 too, as you say here.

First of all, the value of the curvature and the error bar are both dependent on which parameters you allow to run free (e.g. we could peg w at -1)...

Pegging w= -1 is easy to do visually from figure 17. Just draw an horizontal line across the constraints at the w = -1 level. and project down onto the \Omega_k axis.

quick and dirty yes but it gives rough idea.

just graphically, from the figure, pegging at w =-1 gives an interval of
[- 0.031, 0.002] for \Omega_k
which results in an \Omega_{total} interval of
[0.998, 1.031]

I won't ascribe a sigma level to that, just say it is the projection of their dark (most favored) constraint bubble. the qualitative drift is the same.
===================

I think the deviations [from flatness] are expected at the next decimal place.

That is fascinating! Please expand a little. Quite a bit of my time at PF through 2003 and 2004 was spent defending the infinite, perfectly flat universe from people who would come in and claim it was impossible---that an infinite universe could not have resulted from a big bang. And I would say we don't know for sure that it is infinite but the bang COULD have been infinite in spatial extent and the simplest realistic looking model is infinite flat-----and so on.

I've always been a supporter of the mainstream consensus picture at least as the most likely to be right.

Now I find, to my considerable amusement, that mainstream data really is leaning towards an Omega just a wee bit larger than one!
Should we perhaps not SAY this yet should we wait for higher-ups to indicated that it is all right to say it, before we pipe up?

 

[ray b]

voice of america news on this subject

http://www.voanews.com/english/2006-03-17-voa16.cfm

 

[SpaceTiger]

Pegging w= -1 is easy to do visually from figure 17. Just draw an horizontal line across the constraints at the w = -1 level. and project down onto the \Omega_k axis.

It doesn't quite work that way. You have rerun the entire fit on the data to get the new best fit and error bars. They won't be wildly different, but different enough that they might be relevant to this conversation. The parameters in WMAP are often highly degenerate.

That is fascinating! Please expand a little. Quite a bit of my time at PF through 2003 and 2004 was spent defending the infinite, perfectly flat universe from people who would come in and claim it was impossible---that an infinite universe could not have resulted from a big bang. And I would say we don't know for sure that it is infinite but the bang COULD have been infinite in spatial extent and the simplest realistic looking model is infinite flat-----and so on.

Well, I'm afraid I'm not familiar enough with the popular inflationary models to say anything quantitative. The basic idea behind inflation is that it can take a universe with arbitrary geometry and then expand it exponentially such that the observable universe appears flat, despite the geometry on the largest scales. Inflation does not continue indefinitely, however, so it won't lead to perfect flatness. We believe we have a rough idea of the duration of inflation, so we also have a rough idea of how much it flattened the universe. Of course, if the universe started as flat and infinite, then it would remain so after inflation. When I say that inflation "predicts" a deviation from flatness, I'm intrinsically assuming that the universe isn't fine-tuned to be flat.

Now I find, to my considerable amusement, that mainstream data really is leaning towards an Omega just a wee bit larger than one! Should we perhaps not SAY this yet should we wait for higher-ups to indicated that it is all right to say it, before we pipe up?

It doesn't have enough statistical significance to be worth mentioning, both in my opinion and the opinion of the experimenters. It's consistent with a closed, open, or flat universe, but only at about the 1% level (using standard cosmology). I really think that's the best way to put it at this point, and that statement is based on both experience with astronomical results and the interpretations of my superiors. If the deviation becomes 2 or 3 sigma, then people will probably start to take notice. I think that's possible in the next release, though the law of diminishing returns will render the next year or two of WMAP data insigificant compared to the first two releases.

 

[cscott]

Is this it? http://www.nasa.gov/vision/universe/starsgalaxies/wmap_pol.html

 

[Chronos]

I seriously doubt the universe started flat and infinite. I think it has always been close to flat [at least after the first trillionth or so second] and tends toward zero over time.

 

[marcus]

OK, thanks for the help. And thanks in advance for help with this!
We are talking about Spergel et al
http://lambda.gsfc.nasa.gov/product/map/current/map_bibliography.cfm
the "implications for cosmology" article that just appeared

a quick link is
http://lambda.gsfc.nasa.gov/product/map/dr2/pub_papers/threeyear/parameters/wmap_3yr_param.pdfPlease look at page 43 figure17and you will see that the 68% confidence interval for Omega_k is

[-0.037, -0.008]

...[EDIT this is when w, the dark energy equation of state, is allowed to vary and be constrained by the data along with curvature]...

... may be moving towards a picture where we assume Omega_total is a wee bit over unity.

Dear fellow posters! I would like to specialize this thread to consider JUST the "implications for cosmology" paper that I mentioned, and any papers that come out later continuing that same particular line of investigation.

I want to focus on any controversy that arises about Omega_tot, in the wake of WMAP three-year data release. And related issues raised by the "implications for cosmology" paper.

THERE ARE HALF A DOZEN OTHER wmap PAPERS that came out, about other things.

THERE ARE MANY QUESTIONS TO EXPLORE IN OTHER THREADS, if you would care to, as well as general features of the WMAP mission and satellite to discuss.

SPACE-TIGER has initiated a general thread about WMAP and given an excellent overview. You may wish to get in on that thread for a general wide-ranging discussion.

Thanks to Ray B and to CS Scott for the links to general information and press releases. They are the best links of that sort that I have seen to date!

I hope you want to discuss and ask questions related to those links---e.g. about the significance of the polarization data etc.---in which case you might wish to raise those questions with Space Tiger in the thread he started.

Chronos, you are right on topic with what I would like to think about here. We may not be able to GET anywhere, but Omega_tot is a darned interesting issue and we ought to have it out there on the table yes?

 

[marcus]

Focus of this thread

As I said in post #19, I want to focus on the Spergel et al "implications for cosmology" paper

Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology

a quick link is
http://lambda.gsfc.nasa.gov/product/map/dr2/pub_papers/threeyear/parameters/wmap_3yr_param.pdfI see there are 23 authors

THE AUTHORS RAISE THE ISSUE OF A NON-FLAT UNIVERSE in pages 49 thru 57, in their section 7.2 entitled "Non-flat universe".

If you want to discuss on the topic of this thread, please get the PDF of that Spergel et al paper and have a look at pages 49-57.

there is not all that much to read and it's not all that hard.

BTW we should keep in mind that it is a controversial issue. the prevailing view is flat-U. But the 23 authors of Spergel et al left a crack in the door: they put in a section called "Non-flat universe" indicating that it is perhaps just barely legitimate to consider the possibility

please get the PDF, if you have any trouble let me know and i will check the link

*not here at PF, of course, where we thrive on controversy, but maybe in other venues

 

[SpaceTiger]

BTW we should keep in mind that it is a controversial issue. the prevailing view is flat-U, so it would be perfectly understandable if there were a tendency to want to control or suppress* discussion of the mere possibility that the U might not be flat.

Not this again. Nobody's trying to "suppress" discussion of possibilities. In fact, it's you who's insisting on one particular possibility, I'm claiming all three options (open, closed, flat) are possible. What I'm trying to tell you is that you're overinterpreting the data. I'll be more than happy to continue discussing their error analysis, because it seems to be at the root of your misunderstanding.

But the 23 authors of Spergel et al left a crack in the door: they put in a section called "Non-flat universe" indicating that it is perhaps just barely legitimate to consider the possibility

That's right, it's two paragraphs and a bunch of figures. They conclude very simply that \Lambda CDM is consistent with the data. As scientists, we're always considering possibilities, it's our job. We don't, however, make wild claims about non-flatness without actually analyzing the data.

In the coming weeks, we may see some papers that address the issue head-on and perform a more detailed analysis of the flatness issue. If so, I think that's a great topic for discussion. These results, however, are straightforward and we won't be able to distinguish a flat from a non-flat model by staring at their figures.

 

[marcus]

I'm claiming all three options (open, closed, flat) are possible...

I agree

 

[marcus]

"implications for cosmology" paper now on ArXiv

the paper I want to specialize on considering in this thread was posted today on arxiv

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

D. N. Spergel, R. Bean, O. Dore', M. R. Nolta, C. L. Bennett, G. Hinshaw, N. Jarosik, E. Komatsu, L. Page, H. V. Peiris, L. Verde, C. Barnes, M. Halpern, R. S. Hill, A. Kogut, M. Limon, S. S. Meyer, N. Odegard, G. S. Tucker, J. L. Weiland, E. Wollack, E. L. Wright

89 pages, 28 figures, submitted to ApJ

"A simple cosmological model with only six parameters (matter density, Omega_m h^2, baryon density, Omega_b h^2, Hubble Constant, H_0, amplitude of fluctuations, sigma_8, optical depth, tau, and a slope for the scalar perturbation spectrum, n_s) fits not only the three year WMAP temperature and polarization data, but also small scale CMB data, light element abundances, large-scale structure observations, and the supernova luminosity/distance relationship. Using WMAP data only, the best fit values for cosmological parameters for the power-law flat LCDM model are (Omega_m h^2, Omega_b h^2, h, n_s, tau, sigma_8) = (0.127+0.007-0.013, 0.0223+0.0007-0.0009, 0.73 +- 0.03, 0.951+0.015-0.019, 0.09 +- 0.03, 0.74+0.05-0.06). The three year data dramatically shrink the allowed volume in this six-dimensional parameter space. Assuming that the primordial fluctuations are adiabatic with a power law spectrum, the WMAP data_alone_ require dark matter, and a spectral index that is significantly less than the Harrison-Zel'dovich-Peebles scale-invariant spectrum (n_s=1,r=0). Models that suppress large-scale power through a running spectral index or a large-scale cut-off in the power spectrum are a slightly better fit to the WMAP and small scale CMB data than the power-law LCDM model (Delta chi^2 = 3) The combination of WMAP and other astronomical data yields significant constraints on the geometry of the universe, the equation of state of the dark energy, the gravitational wave energy density, and neutrino properties. Consistent with the predictions of simple inflationary theories, we detect no significant deviations from Gaussianity in the CMB maps."

It is substantially the same as what i linked to earlier when it was at the NASA website.

a handful of other paper covering other facets of the data were posted at the same time, and will doubtless be discussed elsewhere

a particular focus of interest for me, in this "implications for cosmology" paper, is page 54
figure 17.

in this figure w (dark energy equation of state) and Omega_k are both allowed to vary and both constrained by the data. When both are constrained to 68 percent confidence, a key parameter Omega_total falls in the interval [1.008, 1.037]
My feeling is that it would be seriously over-interpreting to conclude that Omega = 1 exactly or that the universe is spatially flat. In fact one should probably keep open the possibility that the universe is not spatially flat and that Omega is slightly greater than one.

My hope is that this is not controversial and that we can wait to see how scholarly opinion develops on this issue.

 

[marcus]

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

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.

 

[SpaceTiger]

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.

You're reading too much into their words, especially considering that on page 50, they say:

This figure confirms that our minimal model,
\Omega_k = 0 and w = −1 is consistent with the current data.

Needless to say, \Omega_k=0 is a flat universe.

Also, it should be noted that "consistent with flatness" doesn't negate other possibilities anymore than "consistent with near flatness". Consistency with one model doesn't say anything about consistency with another.

Nobody in the mainstream or on the WMAP team is trying to imply that the universe must be perfectly flat. In fact, one reason we cooked up inflation was so that we didn't have to assume perfect flatness in our models.

 

[marcus]

Nobody in the mainstream or on the WMAP team is trying to imply that the universe must be perfectly flat. In fact, one reason we cooked up inflation was so that we didn't have to assume perfect flatness in our models.

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

You are quite welcome to imagine that I am "reading too much into their words".

As you say yourself, we don't have to assume perfect flatness!

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

No one, certainly not me, is saying this is a certainty.

this is what I said

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.

please YOU do not read into that more than is there.

 

[kmarinas86]

If this is true, then this throws away the notion that a closed universe means a big crunch. So according to the latest evidence, a closed universe could be accelerating and could even lead to a big rip. As far as I know, there is no widely known evidence for a big crunch at this time. Did I get that wrong?

 

[marcus]

If this is true, then this throws away the notion that a closed universe means a big crunch. So according to the latest evidence, a closed universe could be accelerating and could even lead to a big rip. There is no widely known evidence for a big crunch at this time. Did I get that wrong?

In case Space Tiger isn't handy to respond to your question. I will just offer my personal opinion that you did not get it wrong.

I'm not sure what you mean by "this" that is true. But a closed universe in the sense of Omega_total greater than 1, or spatial finiteness certainly does not by itself imply a "big crunch".

A "big rip" is the kind of thing people talk about when they are assuming a version of dark energy with the equation of state number w less than -1.

If dark energy is simply einstein's cosmological constant then w = -1 exactly----no big rip.

That's just my personal opinion. the local experts will no doubt correct me if I am wrong.

BTW hi kmarinas, glad to have company.

 

[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.