As we look forward to the abundance (avalanche!) of high-quality observations that will test Inflation + CDM, we have to make sure the predictions of the theory match the precision of the data. In so doing, CDM + Inflation becomes a ten (or more) parameter theory. For astrophysicists, and especially cosmologists, this is daunting, as it may seem that a ten-parameter theory can be made to fit any set of observations. This is not the case when one has the quality and quantity of data that will be coming. The standard model of particle physics offers an excellent example: it is a nineteen-parameter theory and because of the high-quality of data from experiments at Fermilab's Tevatron, SLAC's SLC, CERN's LEP and other facilities it has been rigorously tested and the parameters measured to a precision of better than 1% in some cases. My worry as an inflationist is not that many different sets of parameters will fit the upcoming data, but rather that no set of parameters will!
In fact, the ten parameters of CDM + Inflation are an opportunity rather than a curse: Because the parameters depend upon the underlying inflationary model and fundamental aspects of the Universe, we have the very real possibility of learning much about the Universe and inflation. The ten parameters can be organized into two groups: cosmological and dark-matter (Dodelson et al, 1996).
3.1. Present status of Inflation + CDM
A useful way to organize the different CDM models is by their dark-matter content; within each CDM family, the cosmological parameters vary. One list of models is:
Figure 3. Summary of viable CDM models, based upon CBR anisotropy and determinations of the present power spectrum of inhomogeneity (Dodelson et al, 1996).
Figure 3 summarizes the viability of these different CDM models, based upon CBR measurements and current determinations of the present power spectrum of inhomogeneity derived from redshift surveys. sCDM is only viable for low values of the Hubble constant (less than 55 km s-1 Mpc-1) and/or significant tilt (deviation from scale invariance); the region of viability for CDM is similar to sCDM, but shifted to larger values of the Hubble constant (as large as 65 km s-1 Mpc-1). CDM has an island of viability around H0 ~ 60 km s-1 Mpc-1 and n ~ 0.95. CDM can tolerate the largest values of the Hubble constant.
Considering other relevant data too - e.g., age of the Universe, determinations of M, measurements of the Hubble constant, and limits to - CDM emerges as the "best-fit CDM model" (Krauss & Turner, 1995; Ostriker & Steinhardt, 1995; Liddle et al, 1996); see Fig. 4. Moreover, its "smoking gun signature," negative q0, has apparently been confirmed (Riess et al, 1998; Perlmutter et al, 1998). Despite my general enthusiasm, I would caution that it is premature to conclude that CDM is anything but the model to take aim at.
Figure 4. Constraints used to determine the best-fit CDM model: PS = large-scale structure + CBR anisotropy; AGE = age of the Universe; CBF = cluster-baryon fraction; and H0= Hubble constant measurements. The best-fit model, indicated by the darkest region, has h 0.60 - 0.65 and 0.55 - 0.65.