# WMAP3 and Spatial Closure

1. Mar 10, 2006

### 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#1391

He 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

Last edited: Mar 10, 2006
2. Mar 10, 2006

### Garth

20-22 March 2006 or 2007?

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

Garth

3. Mar 10, 2006

### EL

:tongue2:
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...

4. Mar 12, 2006

### SpaceTiger

Staff Emeritus
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.

5. Mar 12, 2006

### marcus

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

6. Mar 12, 2006

### wolram

Why, NASA and not the virgin results ?

Last edited: Mar 12, 2006
7. Mar 13, 2006

### SpaceTiger

Staff Emeritus
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/

8. Mar 13, 2006

### SpaceTiger

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

9. Mar 13, 2006

### EL

That's some really exciting news!

10. Mar 14, 2006

### Garth

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

11. Mar 16, 2006

### 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.

12. Mar 16, 2006

### SpaceTiger

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

13. Mar 16, 2006

### marcus

I just looked at Spergel et al paper
http://lambda.gsfc.nasa.gov/product/map/dr2/pub_papers/threeyear/parameters/wmap_3yr_param.pdf

Check 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

Last edited: Mar 16, 2006
14. Mar 16, 2006

### 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...

Last edited: Mar 16, 2006
15. Mar 16, 2006

### 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? thx in advance.

16. Mar 16, 2006

### hellfire

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:

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

17. Mar 16, 2006

### George Jones

Staff Emeritus
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

18. Mar 16, 2006

### marcus

thanks to you both!

19. Mar 17, 2006

### 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.pdf

Please look at page 43 figure17

and 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.

Last edited: Mar 18, 2006
20. Mar 17, 2006

### SpaceTiger

Staff Emeritus
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.