Comparative CMBology: Putting Things Together

I present a series of diagrams which illustrate why the cosmic microwave background (CMB) data favor certain values for the cosmological parameters. Various methods to extract these parameters from CMB and non-CMB observations are forming an ever-tightening network of interlocking constraints. I review the increasingly precise constraints in the Ωm−ΩΛ plane and show why more cosmologists now prefer ΛCDM cosmologies to any other leading model. 1. What is the CMB data trying to tell us? A convenient way to interpret CMB observations is to fit the angular power spectrum of the data to parameter-dependent models. Figure 1 shows the recent CMB measurements along with three such models. In Figure 2, binning of this data reduces the scatter and provides a representative region favored by the data. Important parameters that can be constrained by CMB power spectra include Hubble’s constant h, the cosmological constant ΩΛ, the density of cold dark matter ΩCDM, and the density of baryonic matter Ωb. Figures 1 8 provide a qualitative feel for the lever arm that the CMB data provides for constraining these and other parameters simultaneously. Unless stated otherwise, the models shown have the following default values: h = 0.70, ΩΛ = 0.7, Ωm = ΩCDM + Ωb = 0.3, Ωbh 2 = 0.020, a power spectral index of primordial scalar density fluctuations ns = 1 and an overall normalization Q10 = 18 μK. The grey band in Figure 2 is reproduced in Figures 3 8 and represents the data in a modelindependent way. With it, the eye can pick out which models best fit the data. A reduction in h increases the amplitude of the first peak (Fig. 3). An increase in the number of baryons increases the gravitating mass of the oscillating baryon-photon fluid . This enhances the first peak (Fig. 4) by producing more gravitational compression as the baryons drag the photons further into the potential wells (and further away from the potential hills). The second peak is suppressed because, before decoupling, these smaller scales experienced the same additional compression (and rarefaction) and, at decoupling, we are seeing a subdued rebound from this enhanced compression (and rarefaction), i.e., we are seeing the smaller amplitude of an oscillation whose zero level had been lowered in the previous oscillation by the effect of additional baryons. An increase in Ωm decreases the amplitude of the first peak (Fig. 6). For discussion of the physics of the parameter dependencies of features in the CMB power spectrum see e.g. Hu & Sugiyama (1995), Hu (1995), Tegmark (1996), Lineweaver et al. (1997).