Published in PASP, 111, 274, 1999.
ABSTRACT. We have fossil evidence from the thermal background radiation that our universe expanded from a considerably hotter denser state. We have a well defined, testable, and so far quite successful theoretical description of the expansion: the relativistic Friedmann-Lemaître cosmological model. The observational successes of this model are impressive but I think hardly enough for a convincing scientific case. One way to see the limitations is to compare the lists of observational constraints and free hypotheses within the model; they have similar lengths. Another way to assess the state of the cosmological tests is to consider the search for concordant measures of the mass density parameter and the cosmological constant. The scorecard shows that the high density Einstein-de Sitter model is seriously challenged, but that there is not much to choose between the grades for low mass density models with and without a cosmological constant. That is, it is hard to argue that the Friedmann-Lemaître model is strongly overconstrained, the usual criterion for a mature theory. Work in progress will significantly improve the situation and may at last yield a compelling test. If so, and the Friedmann-Lemaître model survives, it will close one line of research in cosmology: we will know the outlines of what happened as our universe expanded and cooled from high density. It will not end research, of course; some of us will occupy ourselves with the details of how galaxies and other large-scale structures came to be the way they are, others with the issue of what our universe was doing before it was expanding. The former is being driven by rapid observational advances. The latter is being driven mainly by theory, but there are hints of observational guidance.
KEY WORDS: cosmology: theory -- cosmology: observations
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