Figure 10. Measurements of the CMB power spectrum. CMB power spectrum from the world's combined data, including the recent WMAP satellite results (Hinshaw et al. 2003). The amplitudes of the hot and cold spots in the CMB depend on their angular size. Angular size is noted in degrees on the top x axis. The y axis is the power in the temperature fluctuations. No CMB experiment is sensitive to this entire range of angular scale. When the measurements at various angular scales are put together they form the CMB power spectrum. At large angular scales ( 100), the temperature fluctuations are on scales so large that they are `non-causal', i.e., they have physical sizes larger than the distance light could have traveled between the big bang (without inflation) and their age at the time we see them (300,000 years after the big bang). They are either the initial conditions of the Universe or were laid down during an epoch of inflation ~ 10^-35 seconds after the big bang. New data are being added to these points every few months. The concordance model shown has the following cosmological parameters: = 0.743, _CDM = 0.213, _baryon = 0.0436, h = 0.72, n = 0.96, = 0.12 and no hot dark matter (neutrinos) ( is the optical depth to the surface of last scattering). ² fits of this data to such model curves yields the estimates in Table 1. The physics of the acoustic peaks is briefly described in Fig. 11.

Figure 11. The dominant acoustic peaks in the CMB power spectra are caused by the collapse of dark matter over-densities and the oscillation of the photon-baryon fluid into and out of these over-densities. After matter becomes the dominant component of the Universe, at z_eq 3233 (see Table 1), cold dark matter potential wells (gray spots) initiate in-fall and then oscillation of the photon-baryon fluid. The phase of this in-fall and oscillation at z_dec (when photon pressure disappears) determines the amplitude of the power as a function of angular scale. The bulk motion of the photon-baryon fluid produces `Doppler' power out of phase with the adiabatic power. The power spectrum (or Cs) is shown here rotated by 90° compared to Fig. 10. Oscillations in fluids are also known as sound. Adiabatic compressions and rarefactions become visible in the radiation when the baryons decouple from the photons during the interval marked z_dec ( 195 ± 2, Table 1). The resulting bumps in the power spectrum are analogous to the standing waves of a plucked string. This very old music, when converted into the audible range, produces an interesting roar (Whittle 2003). Although the effect of over-densities is shown, we are in the linear regime so under-densities contribute an equal amount. That is, each acoustic peak in the power spectrum is made of equal contributions from hot and cold spots in the CMB maps (Fig. 12). Anisotropies on scales smaller than about 8' are suppressed because they are superimposed on each other over the finite path length of the photon through the surface z_dec.

Figure 12. Full sky temperature map of the cosmic microwave background derived from the WMAP satellite (Bennett et al 2003, Tegmark et al 2003). The disk of the Milky Way runs horizontally through the center of the image but has been almost completely removed from this image. The angular resolution of this map is about 20 times better than its predecessor, the COBE-DMR map in which the hot and cool spots shown here were detected for the first time. The large and small scale power of this map is shown separately in the next figure.