The Doppler Peak

Although called the ``Doppler'' peak the Doppler effect is only one of the mechanisms which contribute to it. The others are intrinsic temperature variations and the early integrated Sachs-Wolfe effect. The reason for the peak is that a perturbation entering the horizon starts to grow in density contrast with the over-dense zones collapsing and the under-dense expanding until the tightly coupled photons can resist gravity via radiation pressure and reverse the direction of the oscillation. This extreme turning point is exactly the where these modes corresponding to the peak find themselves at re-combination.

This scale size of these modes is approximately that of the Hubble radius at re-combination and can be used as a standard ruler so that the geometry of the universe can be deduced by measuring their angular size. The practical result of this is that the spherical harmonic $\ell_{peak}$ at which the peak occurs gives us a measure of the total density $\Omega_0$ of the universe via the relation $\Omega_0 \approx 200/\ell_{peak}$. A flat universe as required by inflation will have a peak at $\ell=200$, but geodesic focusing of an open universe of $\Omega_0 = 0.2$ will shift the peak to nearer $\ell=500$.

One important point of the above effect is that it directly gives the total density of the universe; dark and baryonic matter. Meanwhile the amplitude of the peak can be used to obtain an estimate of the just the baryonic component, since only this part is coupled by Thomson scattering to the photon fluid involved in acoustic oscillations. The amplitude of the effect is proportional to $\Omega_B h^2$, where $\Omega_B$is the baryonic density in units of critical closure density and h is the Hubble tuning factor such that $h = H_0/(100{\rm ~km/s~Mpc}^{-1}$.