How is density calcuated from WMAP data

[Hal King]

The traditional relation used for critical density involves assuming the speed of light as a 'maximum escape velocity' (at least it shows up that way).

So I guess really the question is: Is the WMAP determined density independent of General Relativity or models?

 

[Wallace]

No. The WMAP density (and many other parameters) is model dependent, since the density is just a parameter of the model. The model assumes GR to be true. Depending on what is different in some other theory compared to GR, the WMAP results may imply quite different things, given that theory. WMAP measures many things however, so most theories of gravity that one could propose would not even be self consistent given the WMAP results.

There are many other non-GR theories being considered in cosmology. The first thing that is done for these models is to determine the observational consequences for the different proposed physics. To date, no alternative to GR has been able to re-produce the concordance with all the available data as well as GR (with dark matter and dark energy). That may not always be the case in the future of course.

 

[Hal King]

Thanks, that was the conclusion what I was coming to.

So what does WMAP provide as data that constrains results? Or at least some values that are model less sensitive?

All I see quoted is 'density' or H0. Both seem to be derived and model dependent.

 

[Wallace]

WMAP provides a number of important things. Probably the most important is the angular power spectrum of the anisotropies in the CMB, expressed as the power as a function of angular wave number.

In loose terms, what this means is a measure of the angular size of features in the CMB temperature map. For instance, there is a peak in the spectrum at around 2 degrees (give or take). What this means is that if you look at the WMAP temperature map, a lot of the blobs are about 2 degrees across, as opposed to being randomly distrubuted.

WMAP also measures the polarisation of the CMB, although these measurements are more noisy and not as much has been drawn from them. None the less this information contributes to theories about inflation.

In addition, correlating the features seen by WMAP with galaxy redshift surveys has given strong evidence for the existence of the Integrated Sachs-Wolfe effect (ISW) which is a real 'smoking-gun' for dark energy. Any other theory would have to explain why they also predict this to occur.

Now, to get from these measurements to model dependent constraints (such as density parameters of the FRW model) requires two bits of physics to be worked out. The first is to compute the physical size of the perturbations in the density (and temperature) of the material in the early Universe. The second is to work out the angular size that those features would appear to us, given the cosmological distance laws. Both of these steps require you to assume certain physics in order to compute the results, however getting sensible results out of this process is not trivial, and hence doing this process is a test of the physics and the parameters of a model.

As I said in my first post, the standard model works very well to explain the data. The important thing in terms of physics is not the value of the model parameters (i.e. the density parameters or H_0 ) but more that there are single values of those parameters that fit all the data. That says that the model is consistent and suitable for explaining the data.

So the point of WMAP etc in the end is not the measuring of these parameters for the sake of it, but as a test of the theory. You can compare the parameter values that WMAP gives to that which fit completely different data sets and the values agree, again comfirming that the theory is reasonable.

 

[Hal King]

Thanks for your reply.

Seems to be consistency check for the cosmology models -- and for the application of the appropriate data measurement techniques.

But what is still bothering me is that the 'Standard Model' and General Relativity are actually composed of separate 'pieces' or parts -- meaning that when its said that GR or SM agrees with the results that this is an exaggeration -- it only agrees with certain parts. Often they are never identified.

I have a MAJOR problem with ANY theory that is proposed as a 'theory of everything' -- or anything close to that.

So if you have a new model, where do you go to find out what kind of predictions and in what format is needed for a comparison? i.e. how is a check done against the data?

 

[Wallace]

But what is still bothering me is that the 'Standard Model' and General Relativity are actually composed of separate 'pieces' or parts -- meaning that when its said that GR or SM agrees with the results that this is an exaggeration -- it only agrees with certain parts. Often they are never identified.

What parts are not in agreement with the data? There are indeed some relatively minor, but none the less important problems, such as the density profiles of dark matter haloes in N-body simulations compared to galaxies, or the abundance of dwarf galaxies, but there is a great deal of uncertainty in the modelling in those cases. For things where we can be more confident about our predictions, the data is well described by LCDM. Note that 'standard model' is a bit strong, usually LCDM is known as 'the concordance model' to highlight the fact that the model is concordant with independent data sets, but rests on physics not well understood at the present time. In other words it is a concordant model, but not a true physical theory as such. This is in contrast to the standard model of particle physics, which is a different set of ideas (that none the less is obviously connected to cosmology at some level).

I have a MAJOR problem with ANY theory that is proposed as a 'theory of everything' -- or anything close to that.

Then you will be happy to know that no current theory is described as such, certainly not the current best guess cosmology model. I think you are mixing up theories, and even hypothetical future theories, with each other. The term 'theory of everything' applies to the search for a theory that consistantly describes all the fundamental forces and particles in the Universe. At present the standard model of particles physics is incomplete, because it does not incorporate gravity in a completely consitant way. But this shouldn't be confused with the LCDM model of cosmology. Of course if we were to come up with a theory of everything it should be consitent with (and probably explain in more detail) the LCDM model.

So if you have a new model, where do you go to find out what kind of predictions and in what format is needed for a comparison? i.e. how is a check done against the data?

You need to work out what angular power spectrum your theory predicts, and compared that against the WMAP (and other CMB probes) data. Depending on the nature of the theory existing codes for doing this (CMBFAST, CAMB, CMBeasy are probably the three most widely used) could be converted, but depending on the model and how different it is a tool for this might need to be build from scratch. Note that the WMAP data (as well as plenty of other data) is publicly available.

In addition you would also need to make predictions about the luminosity distance, in order to compare to supernovae type 1a data as well as the angular diameter distance, in order to compare with Baryon Accoustic Oscillation data from galaxy redshift surveys. You would also need to work out the linear perturbation theory to describe the growth of fluctuations in the matter density field in order to compare with results from cluster abundance and galaxy redshift surveys. There's probably some other points I've missed, but that would be a good start.

If a new theory managed to explain all of that data consistantly, and had some theoretical advantage of LCDM, like removing the need for dark energy/matter then that would be very interesting. But without doing that work to show that consistency any talk of alternatives in just barking at the moon. Note that there are plenty of theories that don't have one or both of dark energy and dark matter that are being worked on in the way I've described. Some are promosing, but none have yet managed to do a better job than LCDM. That could change at any point.

 

[Hal King]

Thank you for the information -- particularly about CMBFAST, CAMB, CMBeasy ...

It is sometimes very hard to find out a starting point in a new area.

(And BTW I have seen more that one theory claiming to be one of 'everything' -- just do a web search)

 

[Wallace]

(And BTW I have seen more that one theory claiming to be one of 'everything' -- just do a web search)

If you using a web search to study science you are going to be in trouble! There is a big difference between some guy in his underpants wearing an aluminium hat posting his 'theory' to some site, and mainstream science. Let me make it clear that I am defending the later not the former. In that context there is no theory claimed to be 'the theory of everything'.

 

[Hal King]

That is not so obvious from the outside.

Cosmology seems to have an 'image' problem there. By its nature it tries to describe the entire universe -- using all levels of science from small to large scale. The distinction between scientific cosmology and someones 'theory of everything' is rather vague.

Perhaps that is a discussion that needs to be had?
(Better check on who is wearing the aluminum hat. Hard to tell in the 'dark'.)