Prior Predictions

Models for the angular power spectrum of fluctuations in the microwave background have many free parameters (Seljak & Zaldarriagacmbfast 1996). Many of these parameters are degenerate (Efstathiou & Bond 1999EB), making it possible to fit a wide variety of models to any given data set (e.g., Lange et al. 2000lange). This makes the role of prior constraints, and predictions, particularly important.

Fortunately, the baryon content is the principal component which affects the relative amplitude of the even and odd peaks. For the baryon content specified by the abundances of the light elements and big bang nucleosynthesis (e.g., Tytler et al. 2000tyt), both should be present. However, the even numbered rarefaction peaks should be more prominent when CDM dominates the mass budget. When it does not, baryonic drag suppresses their amplitude (Hu, Sugiyama, & SilkHSS 1997). As declines, the amplitude of the second peak declines with it. In the case where $\Oc \rightarrow 0$, the second peak is expected to have a much smaller amplitude than in (McGaugh 1999mypred), consistent with the hints of a small secondary peak in the (de Bernardis et al. 2000Boom) and MAXIMA-1 data (Hanany et al. 2000maxima).

The predictions for the standard paradigm and the pure baryon case (McGaugh 1999mypred) are shown together with the data in Fig. 1. In addition to the illustrative cases I published previously, I have now carefully chosen parameters (Table 1) which satisfy all the constraints which went into building in the first place (Ostriker & SteinhardtOS; 1995; Turnerdebate 1999), updated to include the recent estimate of $\Ob h^2 = 0.019$ (Tytler et al. 2000tyt). All reasonable variation of the parameters which were considered in prior to the results significantly overpredict the amplitude of the second peak. This is difficult to avoid as long as one remains consistent with big bang nucleosynthesis and cluster baryon fractions (Evrard 1997Gus; Bludman 1998Sid).

In contrast, the prediction for a purely baryonic universe is consistent with the data (Fig. 1). The amplitude of the second peak is predicted to be much lower than in universes dominated by CDM, as observed. The power spectra models in Fig. 1(b) are identical to the models I published previously (McGaugh 1999mypred). The only difference is that I have scaled the geometry to match the precise position of the first peak. This mapping is effectively an adjustment of the angular scale by a factor $\alpha$ so that $\ell \rightarrow \alpha \ell$ (Table 1). The data prefer a geometry which is marginally closed, which leads to $\alpha < 1$. This is equivalent to a small adjustment in the value of (Table 1). Once the geometry is fixed, the rest follows. It is in the shape of the power spectrum, and not in the geometry, in which there is a test of the presence or absence of CDM. I have not adjusted the shape at all from what I predicted in McGaugh (1999mypred): this is as close to a ``no-hands'' model as one can come. The pure baryon models provide a good description of the data.

In addition to the models of McGaugh (1999mypred), I illustrate in Fig. 1(b) a model which adheres to the most recent estimate of $\Ob h^2$(Tytler et al. 2000tyt). In this case I have adjusted to match the position of the first peak so that $\alpha = 1$ (Table 1). The shape of the power spectrum measured by the experiment is well predicted by taking strong priors for , H₀, and so on, with the most important being the pure baryon prior $\Oc = 0$. Simply scaling the pre-existing models with two fit parameters, the amplitude $\Delta T$and the geometry, provides a good fit: $\chi_{\nu}^2 < 1$ (Table 1). The data are consistent with a cosmology in which $\Omega_m = \Ob$ and $\OL \approx 1$.