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As discussed at this meeting by Silk, Wilkinson and Spergel, over the next few years, increasingly more accurate measurements will be made of the fluctuations in the cosmic microwave background (CMB) radiation. The underlying physics governing the shape of the CMB anisotropy spectrum can be described by the interaction of a very tightly coupled fluid composed of electrons and photons before recombination (e.g., Hu & White 1996; Sunyaev & Zel'dovich (1970). Figure 6 shows a plot of the predicted angular power spectrum for CMB anisotropies from Hu, Sugiyama & Silk (1997), computed under the assumption that the fluctuations are Gaussian and adiabatic. The position of the first angular peak is very sensitive to Omega0 (Omegam + OmegaLambda + Omegak).

Figure 6

Figure 6. The angular power spectrum of cosmic microwave background anisotropies assuming adiabatic, nearly scale-invariant models for a range of values of Omega0 and OmegaLambda (Hu, Sugiyama, and Silk 1997; their Figure 4). The Cl values correspond to the squares of the spherical harmonics coefficients. Low l values correspond to large angular scales (l ~ 200° / theta). The position of the first acoustic peak is predicted to be at l ~ 220 OmegaTOT-1/2, and hence, shifts to smaller angular scales for open universes.

For information on cosmological parameters to be extracted from the CMB anisotropies, the following must be true: first, the physical source of these fluctuations must be understood, and second, the sources of systematic error must be eliminated or minimized so that they do not dominate the uncertainties.

Recently it has become clear that almost exact degeneracies exist between various cosmological parameters (e.g., Efstathiou & Bond 1998; Eisenstein, Hu & Tegmark 1998) such that, for example, cosmological models with the same matter density can have the same CMB anisotropies, while having very different geometries. As a result, measurement of CMB anisotropies will, in principle, be able to yield strong constraints on the products Omegam h2 and Omegab h2, but not on the individual values of h (= H0 / 100) and Omegam directly. Hence, earlier suggestions that such cosmological parameters could be measured from CMB anisotropies to precisions of 1% or better (e.g., Bond, Efstathiou & Tegmark 1997) will unfortunately not be realized. However, breaking these degeneracies can be accomplished by using the CMB data in combination with other data, for example, the Sloan survey and type Ia supernovae (e.g. White 1999).

Currently the estimates of the precisions for which cosmological parameters can be extracted from measurements of anisotropies in the CMB are based on models in which the primordial fluctuations are Gaussian and adiabatic, and for which there is no preferred scale. Very detailed predictions can be made for this model, more so than for competing models such as isocurvature baryons or cosmic strings or textures. In the next few years, as the data improve, all of these models will be scrutinized in greater detail.

Important additional constraints may eventually come from polarization measurements (e.g., Zaldarriaga, Spergel & Seljak 1997; Kamionkowski et al. 1997), but these may require the next generation of experiments beyond MAP and Planck. The polarization data may provide a means of breaking some of the degeneracies amongst the cosmological parameters that are present in the temperature data alone. Furthermore, they are sensitive to the presence of a tensor (gravity wave) contribution, and hence can allow a very sensitive test of competing models.

Although it is not yet certain how accurately the cosmological parameters can be extracted from measurements of CMB anisotropies, what is clear is that upcoming, scheduled balloon and space experiments offer an opportunity to probe detailed physics of the early Universe. If current models are correct, the first acoustic peak will be confirmed very shortly and its position accurately measured by balloon experiments even before the launch of MAP. These balloon experiments will soon be followed with the total sky and multi-frequency coverage provided by MAP and Planck. This new era now being entered, of precision CMB anisotropy experiments, is extremely exciting.

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