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3.2 Cosmic microwave background

The discovery by the COBE satellite of temperature anisotropies in the cosmic microwave background [63] inaugurated a new era in the determination of cosmological parameters. To characterize the temperature fluctuations on the sky, we may decompose them into spherical harmonics,

Equation 48 (48)

and express the amount of anisotropy at multipole moment l via the power spectrum,

Equation 49 (49)

Higher multipoles correspond to smaller angular separations on the sky, theta = 180° / l. Within any given family of models, Cl vs. l will depend on the parameters specifying the particular cosmology. Although the case is far from closed, evidence has been mounting in favor of a specific class of models - those based on Gaussian, adiabatic, nearly scale-free perturbations in a universe composed of baryons, radiation, and cold dark matter. (The inflationary universe scenario [21, 22, 23] typically predicts these kinds of perturbations.)

Figure 7

Figure 7. CMB data (binned) and two theoretical curves: the model with a peak at l ~ 200 is a flat matter-dominated universe, while the one with a peak at l ~ 400 is an open matter-dominated universe. From [72].

Although the dependence of the Cl's on the parameters can be intricate, nature has chosen not to test the patience of cosmologists, as one of the easiest features to measure - the location in l of the first ``Doppler peak'', an increase in power due to acoustic oscillations - provides one of the most direct handles on the cosmic energy density, one of the most interesting parameters. The first peak (the one at lowest l) corresponds to the angular scale subtended by the Hubble radius HCMB-1 at the time when the CMB was formed (known variously as ``decoupling'' or ``recombination'' or ``last scattering'') [64]. The angular scale at which we observe this peak is tied to the geometry of the universe: in a negatively (positively) curved universe, photon paths diverge (converge), leading to a larger (smaller) apparent angular size as compared to a flat universe. Since the scale HCMB-1 is set mostly by microphysics, this geometrical effect is dominant, and we can relate the spatial curvature as characterized by Omega to the observed peak in the CMB spectrum via [65, 66, 67]

Equation 50 (50)

More details about the spectrum (height of the peak, features of the secondary peaks) will depend on other cosmological quantities, such as the Hubble constant and the baryon density [68, 69, 70, 71].

Figure 8

Figure 8. Constraints in the OmegaM - OmegaLambda plane from the North American flight of the BOOMERANG microwave background balloon experiment. From [74].

Figure 7 shows a summary of data as of 1998, with various experimental results consolidated into bins, along with two theoretical models. Since that time, the data have continued to accumulate (see for example [73, 74]), and the near future should see a wealth of new results of ever-increasing precision. It is clear from the figure that there is good evidence for a peak at approximately lpeak ~ 200, as predicted in a spatially-flat universe. This result can be made more quantitative by fitting the CMB data to models with different values of OmegaM and OmegaLambda [72, 75, 76, 77, 78] or by combining the CMB data with other sources, such as supernovae or large-scale structure [79, 80, 49, 81, 82, 83, 84, 85]. Figure 8 shows the constraints from the CMB in the OmegaM - OmegaLambda plane, using data from the 1997 test flight of the BOOMERANG experiment [74]. (Although the data used to make this plot are essentially independent of those shown in the previous figure, the constraints obtained are nearly the same.) It is clear that the CMB data provide constraints which are complementary to those obtained using supernovae; the two approaches yield confidence contours which are nearly orthogonal in the OmegaM - OmegaLambda plane. The region of overlap is in the vicinity of (OmegaM, OmegaLambda) = (0.3, 0.7), which we will see below is also consistent with other determinations.

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