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The physical processes that gave rise to cosmic structure leave characteristic and identifiable signatures on the CMB that can be seen by using the CMB as a back light. The key aspects of the CMB as an illumination source are that we know the redshift at which the fluctuations were imprinted and we know the frequency spectrum to high accuracy. Probably the best known examples of using the CMB as a back light are the Sunyaev-Zeldovich (SZ) effects (1972). These were discussed in a companion session by John Carlstrom and so I'll not discuss them here. Instead, I'll focus on the formation of the first stars and on gravitational lensing.

The process of formation of the first stars is not well understood and not well observationally constrained. However, it is known that the intergalactic hydrogen in the universe was predominantly neutral after decoupling and is predominantly ionized now. It was the formation of the first stars that reionized the universe. The free electrons from the reionization leave an imprint on the CMB. It can be shown that scattering by an electron in a quadrupolar radiation background polarizes the CMB. Because this happens at low redshifts, z approx 20, the CMB appears polarized at large angular scales. This effect was seen in the first year WMAP data through the polarization-temperature correlation (Kogut et al. 2003).

With the large angular scale anisotropy, one measures the amount of polarized emission and directly infers an optical depth to polarization, tau. The most likely value from WMAP is tau = 0.17 ± 0.04. In other words, roughly 15% of the CMB photons were rescattered by the formation of the first stars (Zaldarriaga 1997). The redshift of z approx 20 is obtained by integrating back over a completely ionized universe until tau = 0.17 is reached. This corresponds to an age of 200 million years after the bang. There is still much more work to be done to understand the ionization history of the universe.

The reionization suppresses the CMB fluctuations at medium scales but gives rise to a new fluctuations at smaller angular scales through the Ostriker-Vishniac effect (OV, Ostriker & Vishniac 1986). The physics is similar to that of the kinetic SZ effect though is applied to density perturbations instead of clusters per se. In other words, the CMB photons are scattered by ionized gas with some peculiar velocity. The effect has the frequency spectrum of the CMB and must be separated from the primary anisotropy through spatial filtering and higher order statistics. Its measurement is one of the goals of the next generation of experiments. Not only is it of intrinsic interest, but it also will be a new handle on breaking the ns - tau cosmic parameter degeneracy.

The CMB is lensed, like distant galaxies, by the intervening mass distribution. A picture of this is shown in Figure 6. The effect of the lensing is large but it will challenging to separate the intrinsic CMB from what we measure (the lensed CMB). The pursuit is worthwhile because from the lensing one can extract P(k) without bias (Seljak & Zaldarriaga 1999, Okamoto & Hu 2003). To a first approximation, lensing redistributes the phase of the anisotropy and so the power spectra of the lensed and unlensed sky are the same. However, there is also a net redistribution of power and so lensing enhances the angular power spectrum at high l.

Figure 6

Figure 6. The difference between a lensed and unlensed CMB field. The image is 1° on a side. The rms amplitude is a few µK with several peaks reaching 20-30 µK. Note the coherence in the lensed features. Figure courtesy of Uros Seljak.

There are two avenues to detecting lensing. One is through higher order statistics (e.g., the four point function, Bernardeau 1997). Because lensing distorts the intrinsic hot and cold spots, a lensed sky has more complicated statistics than the two-point function that describes the intrinsic anisotropy. One can get a sense for this from Figure 6: the difference map has elongated features. Detection through this method requires a high fidelity map. The other avenue is through the CMB polarization. Lensing distorts the E-mode CMB polarization from the decoupling surface, producing B-modes (Zaldarriaga & Seljak 1998). Indeed, it is the largest B-mode signal at l > 200. In a sense, one uses the polarization to filter out the lensing signal from the intrinsic CMB and OV effects.

A goal for cosmologists over the next few years is to use these probes together to study the growth of cosmic structure as a function of redshift. For example, reionization tells us what's happening at z approx 20, the OV effects and diffuse thermal SZ probe the early stages of structure formation, the kinetic and thermal SZ effects in clusters, and the lensing of the CMB probe the later stages of structure formation. By combining these probes, one estimates that the equation of state, w, can be measured to 10% accuracy and the neutrino mass to 0.1 eV. The new thing is that these determinations will be tied to the CMB and will not rely on galaxy surveys. In addition, there is a rich set of correlations and cross checks between various measurements, both within the CMB and between the CMB and optical lensing, that should permit us to build confidence in any conclusions we may draw.

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