If the models for cosmology and structure formation on which Table 1 is based could be taken as given, the only uncertainties being the astronomy, the constraints on the cosmological parameters would be clear. The long list of evidence for m = 0.25 ± 0.10, in the table and the new results from the SNeIa redshift-magnitude relation and weak lensing, abundantly demonstrates that we live in a low density universe. The CBR demonstrates space sections are flat. Since m is small there has to be a term in the stress-energy tensor that acts like Einstein's cosmological constant. The SNeIa redshift-magnitude result favors a low density flat universe over low density with open geometry ( = 0), at about three standard deviations. That alone is not compelling, considering the hazards of astronomy, but it is an impressive check of what the CBR anisotropy says.
But we should remember that all this depends on models we are supposed to be testing. The dynamical estimates of m in lines 1a and 1b assume the inverse square law of gravity. That is appropriate, because it follows from the relativistic cosmology we are testing. We have a check on this aspect of the theory, from consistency with other observations whose theoretical interpretations depend on m in other ways. The CDM model fitted to observed large-scale structure requires a value of m that agrees with dynamics. This elegant result was an early driver for the adoption of the low density CDM model. But we can't use it as evidence for both the CDM model and the inverse square law; we must turn to other measures. We have two beautiful new results, from weak lensing and the redshift-magnitude relation, that agree with m ~ 0.25. The latter does not exclude m = baryons ~ 0.04; maybe MOND accounts for flat vc(r) but does not affect equation (6) (McGaugh 2000). And if we modified local Newtonian dynamics we might want to modify the physics of the gravitational deflection of light.
There are alternative fits to the CBR anisotropy, with new physics (McGaugh 2000), or conventional physics and an arguably desperate model for early structure formation (Peebles, Seager & Hu 2000). They certainly look a lot less elegant than conventional general relativity theory with the CDM model, but we've changed our ideas of elegance before.
In Section 4 I reviewed two issues in structure formation that I think challenge the CDM model. They may in fact only illustrate the difficulty of interpreting observations of complex systems. It's just possible that they will lead us to some radical adjustment of the models for structure formation and/or cosmology. I don't give much weight to this, because it would mean the model led us to the right m for the wrong reason. Relatively fine adjustments are easier to imagine, of course. With them we must be prepared for fine adjustments of the constraints on parameters such as .
This is quite a tangled web. Progress in applying the many tests, including the mapping the CBR temperature and polarization, will be followed with close attention.
We have an impressive case for the Friedmann-Lemaître cosmology, from the successful fit to the CBR anisotropy and the consistency of the evidence for m ~ 0.25 from a broad range of physics and astronomy. But the cosmological tests certainly are not complete and unambiguous, and since they depend on astronomy the program is not likely to be closed by one critical measurement. Instead, we should expect a continued heavy accumulation of evidence, whose weight will at last unambiguously compel acceptance. We are seeing the accumulation; we all look forward to the outcome.
This work was supported in part by the US National Science Foundation.