University of Chicago

- Introduction
- Temperature Maps
- Thermal History
- Acoustic Oscillations
- Angular Peaks
- First Peak
- Second Peak
- Higher Peaks
- Damping Tail
- Parameter Estimation
- Polarization
- Summary

- Potential fluctuations on all scales
- Each mode oscillates independently
- Modes that are half as long oscillate twice as fast

The final subtlety is that inflation lays down potential fluctuations on all scales. Mathematically we take the potential fluctuation in space and Fourier decompose it into plane waves of various wavelengths. Each of these wave-modes behave independently and so we can think of each individually.

There is however a special relationship between the temporal behavior of modes whose wavenumbers are related by integral multiples:

Because it takes half as long for the fluid to compress
into a potential of half the length scale, the bottom mode in the figure
oscillates exactly twice as fast
as the top mode. Mathematically the frequency of the oscillation
is equal to the wavenumber times the speed of sound: ω=
kc_{s}.