Friday, September 3, 2010
I would like to quickly return to my post on cosmologists loving Fourier/Harmonic space and share another example: the power spectrum of the CMB. The famous power spectrum of the CMB, from which we infer things like: dark matter density, baryon density, expansion rate of the universe, etc... is plotted in harmonic space.
Look at the plot above . On the "top" x-axis you see in fact that the power spectrum is plotted in L space. On the "bottom" x-axis you see what length scales in the sky those L modes correspond to. As you can see, the small L modes represent physics that affected very large scales and the large L modes represent the very small scales.
For example, take the first peak. Physically the first peak is at scales where the universe was just coming into casual contact for the first time. What do I mean. I mean: go outside at night with your protractor. Find two points in the night sky that are separated by one degree. The power spectrum is telling us that, at the time of emission of the CMB, those two points were coming into casual contact for the first time. Until that time, those two points were existing as if the other point didn't exist.
Points in the sky separated by more than one degree were not in casual contact at the time the CMB was created and yet if you look at the power spectrum for these larger scales you will notice there is still some structure. This is what is predicted by inflation. In fact, for the lowest L modes, or angular scales close to 90 degrees, inflation predicts that the power spectrum should be nearly flat with a slight downward tilt which is exactly what is seen.
Lastly, for the high L modes, or for points in the sky less than one degree apart, we see oscillations happening. This makes sense since these points were in casual contact for some time and so the photon-baryon plasma between the two points had plenty of time to interact and cause oscillations that manifest themselves n the oscillatory behavior of the power spectrum for high L modes.
So again, the large and small scale physics at play in the universe is easily visualized in harmonic/Fourier space and cosmologists love this.
(Plot Credit: WMAP Team)