## Monday, September 6, 2010

### Angular scales from the CMB

The physics of the CMB is extremely rich, and I won't do it justice in this series of entries. However, I do want to give one example of how the spectrum of the CMB fluctuations and in particular the location and size of the peaks gives us information about the universe. Let's look at the results from analyzing the CMB maps using the spherical harmonic functions one more time:

As I said last time, this plot tells us about the correlations between different regions of the sky. What exactly does that mean? Well, to the naked eye, the CMB map looks fairly random - some parts are blue, some parts are green, but there's no obvious pattern. What the above graph tells us is that regions of the map separated by 1 degree are actually related to each other. The amplitude of the spherical harmonic with a "frequency" of 1 degree is very high compared to other frequencies, just as the amplitude of the sine curve with the same frequency as the A note was very high when I was decomposing the A chord using Fourier analysis.

The next question to be asked is, "so what?" And the answer relates to stuff I was talking about a while ago in the posts on Gravitational Potential Wells. There, I talked about how early fluctuations in the gravitational potential created oscillations, like balls rolling in and out of a divot. In the early universe, small gravitational fluctuations of all shapes and sizes were created. These fluctuations expanded and contracted, interacting with photons to make hot and cold photons, up until the moment of last scatter when the universe became neutral and no longer interacted with photons at all, creating the CMB. What the large peak at 1 degree in the CMB spectrum tells us is precisely the size of the fluctuation that oscillated one time before the moment of last scatter.

Let me see if I can come up with an analogy for how that works that makes sense. Imagine watching a swimming race where the swimmers do laps in the pool. Let's suppose this race includes swimmers of all abilities, so some are very slow and some are like Michael Phelps. The race starts with all swimmers along the starting line, but as time passes, the swimmers spread out according to their abilities. However, because they have to swim laps, the absolute distance between the swimmers and the starting distance is always less than or equal to the length of the pool - in other words, you can't tell the fast and slow swimmers by how far they are from the start, since there will be times when the fast swimmer is heading back to the start line while the slow swimmer is still at the far end of the pool and vice versa.

Now let's stop the race and have each swimmer stop exactly where they are. They will be spread out all over the pool. But, a few of them will be near the far end of the pool. And some of them, the ones whose pace was exactly right will be exactly at the far end of the pool. If we measure the maximum fluctuation in the position of the swimmers, we find that all the swimmers who exactly swam the full length of the pool have that maximum fluctuation - they are farthest from the start. The CMB measurement is making a similar type of measurement. It measures the size of the gravitational potential well that was maximally expanded when we stopped the race, or when the CMB decoupled from the universe. Therefore, we can calculate the size of the pool - or the size of the universe at the time of last scatter. The location of the first peak in the CMB is like a ruler for the early universe. And that ruler helps us find all that other information I've been talking about.

As usual, I fear I have not fully done the physics justice in this rather slow developing and superficial treatment of the problem. However, I think I'm done with the CMB for now. If you want to learn more about it, I do recommend Professor Wayne Hu's excellent website at http://background.uchicago.edu/~whu/ which explains the CMB much better than I could hope to.