While the first CBI power spectrum had only two points, they were two very important points.
A fundamental prediction of all theories in which the microwave background arises cosmologically at the surface of last scattering is Silk damping (Silk, 1968), the exponential decline in the power
spectrum at large ℓ from photon diffusion. The region of the decline is called the “damping tail”
and is unavoidable if the microwave background anisotropies are of primordial origin. The lack of a damping tail would have been a powerful blow against the canonical model of the universe. The two points in Section 3.5 marked the first time the damping tail was measured and were a confirmation of a major prediction of standard cosmology (see White, 2001, for further discussion).
The Padin et al. (2001a) spectrum appeared at an important time, only a few months after the first BOOMERANG (de Bernardis et al., 2000) and MAXIMA (Hanany et al., 2000) spectra were made public. While the principal result of the two experiments was the first precision determination that the universe was geometrically flat, BOOMERANG, and to a lesser extent MAXIMA, had also fueled intense interest because of the apparent lack of signal in the region past the first acoustic peak at ℓ≃600, where the second peak had been expected. The ratio of the second peak height to the first peak is most sensitive to the physical baryon density in the universe, ΩBh2. If real, the most conservative intepretation of the missing second peak would have been that there was a fairly profound misunderstanding of the cosmic baryon content from big bang nucleosynthesis calculations and deuterium line measurements in the Ly-αforest (Tegmark & Zaldarriaga, 2000), and that ΩBh2 was about 50% higher than previously believed. The measurement by the CBI at ℓ ∼ 600 was nearly a factor of two higher inCℓthan that of BOOMERANG, more in line with the level expected from prior baryon estimates, though a bit high. This was a strong indication that once the CMB experiments converged, the second peak would likely be about at the level expected, which indeed has turned out to be the case. Now, all the major CMB experiments are consistent with each other, and the ΩBh2measured from the CMB (e.g. 0.023±0.003 for combined CMB experiments in Sievers et al., 2003) is in good agreement with that measured using other methods, most notably that of Big Bang Nucleosynthesis (Olive et al., 2000; Burles et al., 1999; Tytler et al., 2000). The resolution to the apparent conflict was that the BOOMERANG beam was larger than expected, washing out power on small scales, MAXIMA was consistent with current estimates, and the CBI data happened to have slightly higher than expected power due to cosmic variance and the small sample of only two fields.
The CBI was also able to do some cosmology with the commissioning data although, because of the small area surveyed, it was perforce somewhat limited. The data set was small enough that we were able to do direct likelihood calculations on a grid of models generated using CMBFAST rather than having to do cosmology using the power spectrum. To do this, rather than integrate a flat spectrum model across a band, we integrateCℓ(ℓ= 2πw)Wij(w) to get the total covariance expected from the CMB. The CBI was able, using only the COBE spectrum as additional information, to rule out intermediate density (Ωtot∼0.5−0.6) cosmologies at the 90% confidence level. The CBI was able to do this using effectively only two points because of the sharp drop between them. The only places standard power spectra have such large drops is either on the tail end of the first peak, or in the damping tail. If the drop after the first peak is atℓ∼600, then Ωtot∼0.3, while if the drop is due to damping after the third peak, then Ωtot ∼1.0. With the additional bit of information that there was a first peak at lowerℓ, but without any details as to that peak position or amplitude, the CBI was able to rule out Ωtot<0.7. Not surprisingly, the CBI also measured a low value for ΩBh2 because of its high value at ℓ ∼600, with a best fit value of ΩBh2=0.009, though the constraint was weak, and the likelihood had only dropped by a factor of 2 at ΩBh2=0.019, and a factor of 3 at ΩBh2=0.03.
Chapter 4
First-Year Observations and Results
The first-year observations and analysis were a major advance over the commissioning data of Chapter 3. In addition to more data on the first two fields, another deep field was added, as well as three larger-area∼2◦×2◦ mosaics. The mosaics provide increasedℓ resolution, revealing the shape of the power spectrum in much more detail than is possible with deep fields. The spectrum extraction pipeline was considerably more sophisticated than that of Padin et al. (2001a) as well.
The window matrices were calculated using a method based on gridding visibilities written by Steve Myers called CBIGRIDR (Myers et al., 2003). The final spectrum extraction from the window matrices and gridded data was done using MLIKELY, written by Carlo Contaldi, and was based on the slow Equation 2.36, though we have since adopted the fast methods of Chapter 2. My main contribution to the first-year papers was extracting the power spectrum from the mosaics using CBIGRIDR/MLIKELY. This included major work on understanding systematic effects in the mosaic spectra and how to correct for them. This chapter describes my contributions to the first- year data analysis and results. In Section 4.1 I describe my calculation of a statistical correction to the estimated noise. The bias comes about when combining data points whose variances have been estimated by scatter internal to the data points. Uncorrected, the noise bias has a major impact on the high-ℓ power spectrum. In Section 4.2 I discuss improvements to the CBIGRIDR/MLIKELY pipeline that substantially increased the speed. Those speed increases allowed us to push out to higher-ℓwith the mosaic spectrum. In Section 4.3 I describe how we deal with sources in the mosaics,
and some unexpected effects from the sources I discovered in the process of doing the mosaic analysis.
In Section 4.5 I describe the data that went into the first-year CBI papers. Finally, in Section 4.6, I describe the final power spectrum from the first-year mosaics and cosmological results from the spectrum.