The successes of the CDM paradigm are remarkable. Except possibly for the density profiles at the centers of dwarf and low surface brightness galaxies, the predictions of CDM appear to be in good agreement with the available observations. The disagreements between predictions and data at galaxy centers appear to occur on smaller scales than was once thought, but as the data improve it is possible that the discrepancies on 1 kpc scales may ultimately show that CDM cannot be the correct theory of structure formation. However, it appears to be better than any alternative theory that has so far been studied, even though these alternative theories have more adjustable parameters.
This article started by discussing the analogy between the effort to understand dark matter and structure formation in modern cosmology and the effort to understand particle physics in the 1960s and 1970s. In both cases, the result was a "standard model" which has guided further work and led to great progress in both theory and observation/experiment. But in both cases, the standard model is not an ultimate theory, and the search is on for a better theory. In the case of particle physics, there is a leading candidate: supersymmetry, and perhaps ultimately string or M theory. Here the analogy fails, because I am not aware of any theory that has all the virtues of CDM but which avoids its possible failure at the centers of galaxies. The quest for such a theory is a worthwhile goal. But for many purposes, including studies of the formation and evolution of galaxies and their large scale distribution, the CDM standard model may still remain very useful. And maybe it is even true.
I learned a great deal about the topics discussed here from my collaborators James Bullock, Avishai Dekel, Ricardo Flores, Anatoly Klypin, Andrey Kravtsov, Ari Maller, Rachel Somerville, and Risa Wechsler, and I also thank Frank van den Bosch, Volker Springel, Rob Swaters, and Simon White for very helpful discussions about the centers of galaxies. This work was supported by grants from NASA and NSF at UCSC, and by a Humboldt Award which supported my visits in fall 2001 to the Max Planck Institutes for Physics in Munich and Astrophysics in Garching, where I thank Leo Stodolsky and Simon White for hospitality. I also thank Aldo Morselli for inviting me to give these lectures at the ISSS, and for his patience waiting for me to send him these notes.