FIG. 1. A map of the CMBR anisotropy as measured by the COBE/DMR radiometers. The temperature range is ±100 µK. A constant level (≈2.73 K) and a dipole distribution have been subtracted to better show the cosmological anisotropies from 10° to 90°. Most of the suppressed dipole is due to the sun’s motion through the reference frame established by the CMBR. The map is in Galactic coordinates, so the Galaxy’s radio emission shows as a bright streak across the middle. Some of the bumps off the Galactic plane are real CMBR anisotropy, some are residual noise.

Earth’s magnetic field affecting the sensitive ferrite switches that alternated the radiometer inputs between two horn antennas pointing 60° apart in the sky. Fortunately, this effect had been seen in balloon-borne experiments using similar radiometer technology, so the switches were magnetically shielded and their susceptibilities measured in preflight testing. Even so, the magnetically induced signal was comparable to the CMBR signal in some radiometers and an empirical correction was needed. Another concern was the magnitude of 300 K Earth emission that diffracted over, or leaked through, COBE’s ground screen. This had not been measured in preflight tests, only estimated from crude (by today’s standards) calculations. The experimental strategy of using several levels of “Dicke” switching caused systematic effects to enter the data stream with different time signatures than that of a sky signal. Switching between antennas at 100 Hz, rotating the spacecraft with a period of 1.25 min, and circling the Earth once every 103 min ensures that systematic effects have a different time signature than that of a true sky signal. For example, the magnetic effect will be largest when mapped in a coordinate system fixed to BEARTH rather than sky coordinates. For those who worry about such things the most important papers associated with COBE’s anisotropy detection are the ones describing the systematic error analysis (4, 5).

Another concern with the COBE/DMR detection of CMBR anisotropy was the issue of foreground microwave emission from our Galaxy (6, 7). Measurements by radiometers at three different frequencies, all with 7° beams on the sky, were used to separate CMBR anisotropies from foreground emission. The CMBR has a different spectrum from those of known Galactic radiation sources—synchrotron, bremsstrahlung, and 20 K dust emissions. At a level of 30 µK the Galactic emission in the COBE/DMR bands could not be estimated from sky maps at higher and lower frequencies, so the COBE/ DMR data itself had to be used to estimate the Galactic contribution. Fig. 1 clearly shows very bright foreground signals associated with the Galactic plane, but the COBE/ DMR data show that for regions more than 20° from the Galactic plane, the sky fluctuations are dominated by CMBR anisotropies. Luckily, we live in a Galaxy whose microwave brightness is five orders of magnitude weaker than the CMBR radiation at wavelengths near 3 mm. Coincidentally, the peak of the CMBR blackbody spectrum is nearby, at about 2 mm wavelength.

Anisotropies at Angular Scales Smaller than 10°: Predictions

To see the effects of physical processes at the decoupling epoch (age t≈3×105 years, redshift z=1,400), we must measure regions of space that were connected by light speed (causal) at that time. In the standard cosmological model causal events at decoupling are separated by less than about 1° as seen now. Numerical integration of the behavior of matter and radiation through the decoupling epoch have long shown (8) that structure should be expected in the angular power spectrum of anisotropies at scales below a few degrees (9). Recent analytic work on the decoupling process (10) has shown that most of the CMBR anisotropy is caused by acoustic oscillations in the ionized fluid as the universe expands and cools. The scale of the oscillating regions is determined by the speed of sound which in turn is set by the density and composition of the fluid. This is the idea behind using medium-scale anisotropy measurements to test the detailed physics of the cosmological model and, if a model fits the data, to measure the values of some cosmological parameters.

The physics is deceptively simple. During decoupling, as the fluid is still partially ionized, radiation and matter are still coupled, but the coupling is growing weaker as the matter recombines. The acoustical oscillations are caused by mass falling into relatively over-dense regions [caused by clumped dark matter in cold dark matter (CDM) models]. The radiation is compressed like a spring, eventually causing the fluid to rebound and expand. Meanwhile the optical depth of the fluid is decreasing and more and more photons are scattering for the last time. The phase of the fluid oscillation when photons are scattered for the last time determines whether their temperatures will be slightly above or below the mean CMBR temperature. There are several effects that shift the photon frequency, and hence the CMBR temperature. If the photons are scattered for the last time from a compressed region, adiabatic fluctuations imply a higher temperature, but gravitational redshift will cool the CMBR photons as they climb out of the potential wells. If, however, the region is expanding at that time the scattered photons will be blue shifted by the Doppler effect. The gravitational and Doppler effects are 90° out of phase, so they may tend to reinforce or cancel one another. The angular scale of the oscillations that cause CMBR anisotropy is determined by the sound horizon of the fluid at the decoupling epoch. The phase of an oscillation at last scattering is set by its period and the time between when a scale enters the horizon and when the CMBR photon last scatters. Some acoustical oscillation scales release the photons when they are near the extremes of compression or expansion causing these scales to have a larger rms δT than others. Therefore, a measurement of the rms δT vs. angular size—the anisotropy power spectrum—is expected to have peaks from about 1° to 10′.

The detailed shape of the medium-scale anisotropy power spectrum depends on the cosmological model, the constants of that model, and the detailed physics of decoupling. Some predicted peaks are shown in Fig. 2 for various cosmological models of current interest. Accurate measurements of the angular power spectrum can be used to determine the important cosmological parameters of the model (11, 12). For example, the baryon density and Hubble constant, ΩB and H0. largely determine the height of the first peak and the ratio between peak heights. The total mass density, Ω0, and H0 largely determine the angles at which the peaks occur. Is there, after all. a significant cosmological constant, Λ, in our universe today? Fig. 2 shows that such a model is easily detectable by a well-measured anisotropy power spectrum. A major issue in cosmology research is the whether the universe is open (ΩTOTAL<1) or closed, perhaps with a large density of unidentified CDM. Finally, what is the nature of those initial perturbations? Are they adiabatic or isocurvature? Again Fig. 2 indicates that accurate measurements of the anisotropy power spectrum can distinguish between these various models. Theoretical cosmologists continue to work out the possible consequences of accurate measurements of the anisotropy



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