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Acoustic Oscillations and CMB Anisotropies

The oscillations in the apparent temperature of the primordial plasma were responsible for most of the observed structure in the CMB power spectra shown in Figure 1.6.  Earthbound telescopes observe from a single point in space, so the measured temperature anisotropies of the CMB are approximately the variations in the apparent temperature of the plasma at decoupling. At progressively smaller angular scales on the sky (higher l), the observed modes have smaller wavelengths, so they began oscillating earlier prior to decoupling, and at decoupling they had progressed through more oscillations, yielding the familiar pattern of acoustic peaks in the power spectrum of the temperature variations.  

The oscillations in the plasma were responsible for the peaks in the polarization power spectrum as well.  As the material oscillated back and forth between the overdense and underdense regions, the magnitude of the velocities in the plasma rose and fell 90o out of phase with the oscillations in the apparent temperature variation (The material hardly moved when the apparent temperature variations were large and the restoring force was reversing the direction of flow, and conversely the velocities were large when the apparent temperature variation was nearly zero).  The polarization power spectrum therefore has peaks where the temperature power spectrum has troughs, and vice versa. The peaks in the polarization power spectrum are significantly lower than those of the temperature anisotropies because the thermalizing effect of Thomson scattering discussed in Section 1.1 greatly reduced the efficiency of converting velocity perturbations into cosmological polarization.

If the plasma were an ideal fluid, there would be fluctuations in the temperature and polarization of the CMB on infinitely small scales. However, the fluid was not ideal, and the photons propagated finite distances between scattering events. On distances shorter than this mean free path (which became large at decoupling), variations in the temperature and polarization of the photon gas were suppressed, resulting in the damping tails at high l apparent in both power spectra.

This short, qualitative summary of the physics behind the CMB anisotropies is enough to demonstrate that the temperature and polarization anisotropies are connected through sensible physical processes (see Figure 1.9), and that it is reasonable to use the existing measurements of the temperature anistropies as a guide for estimating the size of the cosmological polarization. The TOCO, BOOMERanG, MAXIMA and DASI temperature anisotropy experiments all show a strong peak in the power spectrum with a peak amplitude of about K at angular scales of about 0.5o, which implies a flat universe with a significant cosmological constant. The location of this first acoustic peak also sets the angular scale of the expected peaks in the polarization power spectrum, and the height of the measured peak indicates the strength of the polarized component. The cosmological polarization therefore should be largest on sub-degree angular scales, where it will be roughly 5uK rms at most (Figure 1.6).

The Origin of Cosmological Polarization

The Structure of Cosmological Polarization

        Power Spectra and the Structure of CMB Anisotropies

        Initial Conditions and Inflation

        The Evolution of Perturbations and Acoustic Oscillations

        Acoustic Oscillations and Apparent Temperature Variations

        Acoustic Oscillations and CMB Anisotropies


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CAPMAP is supported by the Kavli Institute for Cosmological Physics at the University of Chicago.