# Photon-to-baryon ratio from CMB structure details?

## Main Question or Discussion Point

Not sure if this is an easy question or not.

The Wikipedia entry on the Big Bang, in its section on "Abundance of primordial elements," cites the 1988 book by Kolb and Turner (The Early Universe), in saying that the ratio of photons to baryons "can be calculated independently from the detailed structure of CMB fluctuations."

I assume by "structure" they mean its spatial Fourier transform peaks, as shown in the Wikipedia article on CMB, under "Primary anisotropy" - the graph is titled "The power spectrum of the CMB radiation temperature anisotropy in terms of the angular scale (or multipole moment)."

The question is, how do they determine that photon to baryon ratio? (I thought I might save myself the trouble of going to a library and consulting Kolb and Turner.)

## Answers and Replies

nicksauce
Science Advisor
Homework Helper
Very roughly speaking: The first peak in the CMB corresponds to the size of the sound horizon at last scattering, as it is the largest coherent structure in the universe at that time. The sound speed at last scattering is not the usual c / sqrt(3) for a photon gas, but rather it is less because the plasma is "weighed down" by baryons. The sound speed directly depends on the baryon to photon ratio.

Thanks, Nick. Googling "sound horizon at last scattering" gave me lots of sites to explore. One further question while I've got you on-line. How much of this analysis depends on the actual density (of photons and baryons) being taken to be that which is required for nucleosynthesis (and which can be inferred from the Hubble Constant and taking time back to the presumed beginning)?

nicksauce
Science Advisor
Homework Helper
My interpretation is that CMB analysis doesn't depend at all on BBN, and they completely independently give consistent results. However, I do not claim to be an expert and I could very well be wrong.

Thanks again, Nick.

Nick, I apologize for dragging this on, especially when further rumination on my part might allow me to answer my own questions, but one more question occurred to me that you may be able to answer easily. Do you think the CMB analysis depends on the assumption that the expansion is real, and therefore that the matter and photons we assume produced the CMB were, at ~13.7 billion years ago (BYA), much more densely packed in space than they are today? In other words, is there anything inherent in the blackbody radiation, and its spatial variations in temperature, that says "this is due to baryons having X spatial density, and photons having 10,000,000 (or whatever) X"? Moreover, the "sound" speed they're using is undoubtedly geared toward a distance scale, 13.7 BYA, that is much smaller than one would assume for a non-expanding universe. Those are some of the assumptions I assume they made. Without those, I assume the explanation for the structure of the inhomogeneities would be quite different. But, I assume a much more diffuse gas could also display oscillations on a much larger scale somehow.

nicksauce
Science Advisor
Homework Helper
I believe it is correct to say that any WMAP results rely on the assumption that the universe described by the perturbed FRW metric is "true" (i.e., that the expansion is real), and those results give best fit parameters to that universe.