What Is the Ratio of Baryonic to Dark Matter in the CMB?

[Philosopha]

What is the observed DM ratio in CMB ?

Is there observational evidence for the DM ratio in the CMB? Other then the info-graph from Wikipedia which I was explained is based on the assumption of DM being the same total amount back then but the mass of relativistic particles was higher.

Would the 'observed' ratio be 5:1 ? or 2:1 as of Wikipedia ?

 

[fzero]

The first few posts in this older thread appears to answer the question of how this ratio is experimentally determined.

I'm not sure what you mean by "mass of relativistic particles was higher," if a particle is relativistic, then it is a very good approximation to ignore its mass. Perhaps you are thinking of something other than rest mass, but in any case, I do not understand what it might have to do with the difference between baryonic and dark matter.

The observed quantities are what they are, in this case, 5:1 is the present ratio. The cosmological model that is the best fit to the measurements can be used to run this value back to earlier times, which is how the 2:1 value at recombination is obtained.

 

[Philosopha]

Wikipedia showes a "mass" (not particle!) ratio of 2:1 at the time when the CMB was emitted. The graph includes a large portion of photon/neutrino mass thus tipping the ratio to 2:1, if including these particles. A friend already explained to me that this was so, because Photons at that age had a much higher energy than today, therefore the higher mass in the wikipedia graph by the mass equivalence.

http://en.wikipedia.org/wiki/Dark_matter

However, the pressure imprint is caused by baryonic pressur against photons. So it should only be the mass of baryon to DM ratio in the CMB that matters for what we see? So we should 'see' a ratio of 63:12 (5:1) baryons to DM? Is that what we see experimentally? I couldn't find info on that and was just wondering if that was the actual case.

 

[fzero]

Wikipedia showes a "mass" (not particle!) ratio of 2:1 at the time when the CMB was emitted. The graph includes a large portion of photon/neutrino mass thus tipping the ratio to 2:1, if including these particles. A friend already explained to me that this was so, because Photons at that age had a much higher energy than today, therefore the higher mass in the wikipedia graph by the mass equivalence.

http://en.wikipedia.org/wiki/Dark_matter

OK, I understand the terminology. It is more common to quantify the cosmological sources by their energy density. It doesn't really make sense to say that this is equivalent to mass for photons, but for nonrelativistic particles, most of the energy is in the mass.

However, the pressure imprint is caused by baryonic pressur against photons. So it should only be the mass of baryon to DM ratio in the CMB that matters for what we see? So we should 'see' a ratio of 63:12 (5:1) baryons to DM? Is that what we see experimentally? I couldn't find info on that and was just wondering if that was the actual case.

I believe that the pressure term in the equation of state for baryonic and nonbaryonic matter is set to zero in these calculations. There is some discussion in this thread, but basically it's just understood that a contribution from pressure, even for baryons, is much smaller than the experimental precision, so we wouldn't gain anything from adding it. On much smaller scales relevant to astrophysics of stars and the like, of course we can't ignore the pressure.

Now, the way the energy densities appear is through the Friedmann equation as appears in this section:

$$\frac{H^2}{H_0^2} = \Omega_R a^{-4} + \Omega_M a^{-3} + \Omega_k a^{-2} + \Omega_{\Lambda}.$$

Here $\Omega_M$ is the combined baryonic and dark matter contribution. So the first-order measurements don't determine the relative amounts of baryonic vs. dark matter.

The way the dark matter % is determined is to look at the anisotropy of the CMB. There is now a contribution from the interaction between photons and baryons at the surface of last scattering. I am not familiar with the detailed description of this part of the modeling, but there is an interesting http://lambda.gsfc.nasa.gov/education/cmb_plotter/ that let's you tune the cosmological parameters to match the observed power spectrum. Hu and White seems like an important reference for the technical details.