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Our intention is to supplement recent discussions of parameter determinations within the standard relativistic cosmology 58 with a broader consideration of the issues summarized in two questions: what is the purpose of the cosmological tests, and how well is the purpose addressed by recent advances and work in progress?

The short answer to the first question used to be that we seek to check the underlying physical theory, general relativity, applied on the time and length scales of cosmology; the model for the stress-energy tensor in Einstein's field equation, suitably averaged over the rich small-scale structure we cannot describe in any detail; and the boundary condition, that the universe we can observe is close to homogeneous and isotropic on the scale of the Hubble length. Recent advances make use of the CDM prescription for the stress-energy tensor and the boundary condition, so we must add the elements of the CDM model to the physics to be checked.

The short answer to the second question is that we now have searching checks of the standard cosmology, which the model passes. But we believe it takes nothing away from the remarkable advances of the tests, and the exemplary care in the measurements, to note that there is a lot of room for systematic errors. As we discussed in Sec. I.A, the empirical basis for the standard model for cosmology is not nearly as substantial as is the empirical basis for the standard model for particle physics: in cosmology it is not yet a matter of measuring parameters in a well-established physical theory.

We comment on the two main pieces of physics, general relativity and the CDM model, in Secs. IV.A.1 and IV.A.2. In Sec. IV.B we discuss the state of 13 cosmological tests, proceeding roughly in order of increasing model dependence. We conclude that there is a well-established scientific case for the physical significance of the matter density parameter, and for the result of the measurements, 0.15 ltapprox OmegaM0 ltapprox 0.4 (in the sense of a two standard deviation range). Our reasoning is summarized in Sec. IV.C, along with an explanation of why we are not so sure about the detection of Lambda or dark energy.

58 See Bahcall et al. (1999), Schindler (2001), Sarkar (2002), Freedman (2002), Plionis (2002), and references therein. Back.

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