Using WMAP to measure the Hubble's constant

[ta66505477]

How can people measure the Hubble's constant using WMAP?

I found a journal named First-Year Wilkinson Microwave Anisotropy Probe (WMAP)* Observations: Determination of Cosmological Parameters
http://iopscience.iop.org/0067-0049/148/1/175

In 4.1 said
CMB observations do not directly measure the local expansion rate of the Universe rather they
measure the conformal distance to the decoupling surface and the matter-radiation ratio through the amplitude of the early Integrated Sachs Wolfe (ISW) contribution relative to the height of the first peak.

I feel confusing why I cannot get the Hubble's constant directly from WMAP? (but the people always say they can get all the parameters in WMAP)

I am only a year three student and do not have much cosmology background.

 

[marcus]

... constant directly from WMAP? (but the people always say they can get all the parameters in WMAP)
...

I never heard anyone say that you can get all cosmology parameters from CMB observation.

The Hubble parameter is measured from OTHER data, not data on CMB collected by WMAP.

But when I want to look up parameters I often go to a WMAP report, and give a link to a WMAP report, because these are major, recent, comprehensive reports that bring together estimates from OTHER data.

Like Supernova (SN) data.

If you go to a WMAP report and look at one of their tables of numbers, it might say "this is based on WMAP+BAO+SN". That means based not only on CMB data but also on optical telescope counts of galaxies and also on SN. That would be for some other parameter, not Hubble, but is just an example. The authors bring several bunches of data together.

How you measure the Hubble parameter is you compare redshift and brightness of a "standard candle". An example of a standard candle is a certain type of SN which always explodes with approximately the same release of energy. So how bright it looks tells you its actual distance as of today. And then you compare that with the amount the wavelengths are shifted by distance expansion.

Or you use some other "standard candle"---not a supernova but something else of known wattage, so that you can tell the distance from how bright it looks.
=======================

You may have seen people citing WMAP reports as a reliable reference for their numbers, and you might have gotten the wrong impression that this means all those quoted numbers are coming from Cosmic Microwave Background data.

Just because they are published in a WMAP report does not mean they all come from CMB data.

 

[Chalnoth]

I feel confusing why I cannot get the Hubble's constant directly from WMAP? (but the people always say they can get all the parameters in WMAP)

I am only a year three student and do not have much cosmology background.

Well, a sort of basic way to understand this is that it is possible to change spatial curvature, the Hubble constant, and the amount of dark energy together in a way that makes almost no change whatsoever to the CMB power spectrum. Planck may help with this somewhat, but really the best way to fix this is to fix one of the three parameters either by fiat (e.g. by some belief that the spatial curvature really must be zero) or through the use of other experiments.

A physical way to understand this is that the spatial curvature, the Hubble constant, and dark energy don't do much of anything to the physics before the CMB was emitted. Instead they change the way the CMB looks. And it turns out that the three can be varied together to produce almost no change in the appearance of the CMB.

 

[RUTA]

All I see in the way of data for WMAP is temperature vs angular position (direction in sky) and polarization data around hot and cold spots. Am I missing something? If not, that strikes me as a very rarefied source for determining cosmological parameters. Can someone point me to textbook computations using WMAP data? I haven't found anything on line or in their arXiv papers that allows me to reproduce their calculations of flatness, Ho, etc.

 

[Chalnoth]

All I see in the way of data for WMAP is temperature vs angular position (direction in sky) and polarization data around hot and cold spots. Am I missing something? If not, that strikes me as a very rarefied source for determining cosmological parameters. Can someone point me to textbook computations using WMAP data? I haven't found anything on line or in their arXiv papers that allows me to reproduce their calculations of flatness, Ho, etc.

The power of the CMB for determining cosmological parameters lies in the power spectrum of the CMB. The power spectrum is a measure of the average amplitude of fluctuations of a given angular size. It looks like this:
http://lambda.gsfc.nasa.gov/product...nyear/powspectra/images/med/dl7_f01_PPT_M.png

On the left side of the plot are large angular scales. On the right side are small angular scales. The first peak is the sound horizon: overdense areas that were that large at the time of the big bang had just enough time to collapse inward by the time the CMB was emitted.

The second peak is at about half the distance. It's from regions that were small enough to collapse and then bounce back. However, it is only the normal matter that interacts with light and experiences the pressure from light, and so only the normal matter that bounces. The dark matter doesn't bounce. So the second peak is suppressed dramatically compared to the first.

The third peak, like the first peak, has contributions from both normal matter and dark matter. This is the stuff that for normal matter there was enough time for the matter to fall in, bounce back, then fall back in. The dark matter just falls in. So it's larger again. It's much smaller than the first peak because there's an overall trend towards smaller amplitudes. As you can see, the fourth peak gets really small again. Because of this particular effect, the CMB is our most sensitive measurement (by far) of the ratio of normal matter to dark matter.

A number of other various cosmological parameter change the power spectrum in various different ways. Max Tegamark has a nice (but old) site which has a series of movies that show how different parameters change the spectrum:
http://space.mit.edu/home/tegmark/cmb/movies.html

 

[RUTA]

The power of the CMB for determining cosmological parameters lies in the power spectrum of the CMB. The power spectrum is a measure of the average amplitude of fluctuations of a given angular size. It looks like this:
http://lambda.gsfc.nasa.gov/product...nyear/powspectra/images/med/dl7_f01_PPT_M.png

Thanks, how do you calculate that red curve?

 

[ta66505477]

it helps me a lot!
thx everyone.

and one more question. I am reading the cosmological constant that is different between the observation and theory.

By theory, they use something called vacuum energy which came from quantum mechanics. I cannot understand why vacuum energy can be a result of dark energy? I don't know the link between them.

 

[Chalnoth]

Thanks, how do you calculate that red curve?

Haha, well, not easily! Basically it requires a model of the early universe. A simplified model of inflation is used to generate the initial density fluctuations. Then those fluctuations are evolved forward in time using a model of the contents of the universe. The power spectrum is then predicted from this model of the early universe, using its contents and General Relativity to evolve those fluctuations forward in time to what we see in the CMB.

 

[RUTA]

Haha, well, not easily! Basically it requires a model of the early universe. A simplified model of inflation is used to generate the initial density fluctuations. Then those fluctuations are evolved forward in time using a model of the contents of the universe. The power spectrum is then predicted from this model of the early universe, using its contents and General Relativity to evolve those fluctuations forward in time to what we see in the CMB.

Thanks again. I need the explicit calculations so I can learn to calculate that red curve myself. Do you have a reference for a grad textbook, for example?

 

[Chalnoth]

Thanks again. I need the explicit calculations so I can learn to calculate that red curve myself. Do you have a reference for a grad textbook, for example?

Well, one of the premier codes for calculating this stuff a while ago was CMBFast, which is described here:
http://iopscience.iop.org/0067-0049/129/2/431/50929.text.html

I wouldn't recommend actually using that code, though. CAMB is pretty good, but it can be horrible to compile. WMAP's Lambda website has a nice overview of the various software tools that people use:
http://lambda.gsfc.nasa.gov/toolbox/

 

[RUTA]

Well, one of the premier codes for calculating this stuff a while ago was CMBFast, which is described here:
http://iopscience.iop.org/0067-0049/129/2/431/50929.text.html

I wouldn't recommend actually using that code, though. CAMB is pretty good, but it can be horrible to compile. WMAP's Lambda website has a nice overview of the various software tools that people use:
http://lambda.gsfc.nasa.gov/toolbox/

The first link is more what I'm looking for. I don't want to simply play with computational codes that others have written, I want to understand the formalism behind their code so I can write my own. That way I can make modifications to the various assumptions to explore new theories. Here are two excerpts from that first link that I need explained:

The code is based on the integral solution of the transport equation for the photons, the Boltzmann equation.

To calculate the CMB power spectrum, Cl, we need to evolve the perturbations in the different species (cold dark matter, baryons, photons, neutrinos). The perturbations are so small that linear theory suffices. The standard method is first to expand all perturbations in eigenvalues of the Laplacian, which evolve independently. In a flat spacetime this is a Fourier expansion. The wavenumber labels the different eigenmodes. The fluctuations produced by each mode can be calculated separately, and then all the contributions to the power are added, ... Eq (3).

I can order the first few papers cited in this article (didn't find any of them in arXiv), but they don't look promising (Phys Rev Lett, ApJ or MNRAS, for example, aren't going to be pedagogical). Pretend I'm a physics grad student just starting research on this topic and the ultimate goal of my thesis is to find a fit to the WMAP data that uses ... oh, say, a different transport equation for photons or a non-GR approach to gravity. To do that I would need to know exactly what is being done to generate the red curve so I would know exactly what has to be changed.

 

[Chalnoth]

The first link is more what I'm looking for. I don't want to simply play with computational codes that others have written, I want to understand the formalism behind their code so I can write my own. That way I can make modifications to the various assumptions to explore new theories. Here are two excerpts from that first link that I need explained:

The code is based on the integral solution of the transport equation for the photons, the Boltzmann equation.

To calculate the CMB power spectrum, Cl, we need to evolve the perturbations in the different species (cold dark matter, baryons, photons, neutrinos). The perturbations are so small that linear theory suffices. The standard method is first to expand all perturbations in eigenvalues of the Laplacian, which evolve independently. In a flat spacetime this is a Fourier expansion. The wavenumber labels the different eigenmodes. The fluctuations produced by each mode can be calculated separately, and then all the contributions to the power are added, ... Eq (3).

I can order the first few papers cited in this article (didn't find any of them in arXiv), but they don't look promising (Phys Rev Lett, ApJ or MNRAS, for example, aren't going to be pedagogical). Pretend I'm a physics grad student just starting research on this topic and the ultimate goal of my thesis is to find a fit to the WMAP data that uses ... oh, say, a different transport equation for photons or a non-GR approach to gravity. To do that I would need to know exactly what is being done to generate the red curve so I would know exactly what has to be changed.

In practice, however, it's usually better to make use of an existing code and modify it.

As for the specific papers, you can usually get them for free if you just fire off an e-mail to the lead author, if you don't have subscription access. I'd also suggest looking the papers up on SPIRES or NASA ADS to make sure there isn't a free version available.