B. The tests

The literature on the cosmological tests is enormous compared to what it was just a decade ago, and growing. Our references to this literature are much sparser than in Sec. III, on the principle that no matter how complete the list it will be out of date by the time this review is published. For the same reason, we do not attempt to present the best values of the cosmological parameters based on their joint fit to the full suite of present measurements. The situation will continue to evolve as the measurements improve, and the state of the art is best followed on astro-ph. We do take it to be our assignment to consider what the tests are testing, and to assess the directions the results seem to be leading us. The latter causes us to return many times to two results that seem secure because they are so well checked by independent lines of evidence, as follows.

First, at the present state of the tests, optically selected galaxies are useful mass tracers. By that we mean the assumption that visible galaxies trace mass does not seriously degrade the accuracy of analyses of the observations. This will change as the measurements improve, of course, but the case is good enough now that we suspect the evidence will continue to be that optically selected galaxies are good indicators of where most of the mass is at the present epoch. Second, the mass density in matter is significantly less than the critical Einstein-de Sitter value. The case is compelling because it is supported by so many different lines of evidence (as summarized in Sec. IV.C). Each could be compromised by systematic error, to be sure, but it seems quite unlikely the evidence could be so consistent yet misleading. A judgement of the range of likely values of the mass density is more difficult. Our estimate, based on the measurements we most trust, is

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and we would put the central value at _M0 0.25. The spread is meant in the sense of two standard deviations: we would be surprised to find _M0 is outside this range.

Several other policy decisions should be noted. The first is that we do not comment on tests that have been considered but not yet applied in a substantial campaign of measurements. A widely discussed example is the Alcock and Paczynski (1979) comparison of the apparent depth and width of a system from its angular size and depth in redshift.

In analyses of the tests of models for evolving dark energy density, simplicity recommends the XCDM parametrization with a single constant parameter w_X, as is demonstrated by the large number of recent papers on this approach. But the more complete physics recommends the scalar field model with an inverse power-law potential. This includes the response of the spatial distribution of the dark energy to the peculiar gravitational field. Thus our comments on variable dark energy density are more heavily weighted to the scalar field model than is the case in the recent literature.

The gravitational deflection of light appears not only as a tool in cosmological tests, as gravitational lensing, but also as a source of systematic error. The gravitational deflections caused by mass concentrations magnify the image of a galaxy along a line of sight where the mass density is larger than the average, and reduce the solid angle of the image when the mass density along the line of sight is low. The observed energy flux density is proportional to the solid angle (because the surface brightness, erg cm^-2 s^-1 ster^-1 Hz^-1, is conserved at fixed redshift). Selection can be biased either way, by the magnification effect or by obscuration by the dust that tends to accompany mass. ⁽⁶⁷⁾ When the tests are more precise we will have to correct them for these biases, through models for the mass distribution (as in Premadi et al., 2001), and the measurements of the associated gravitational shear of the shapes of the galaxy images. But the biases seem to be small and will not be discussed here.

And finally, as the cosmological tests improve a satisfactory application will require a joint fit of all of the parameters to all of the relevant measurements and constraints. Until recently it made sense to impose prior conditions, most famously the hope that if the universe is not well described by the Einstein-de Sitter model then surely it is the case either that is negligibly small or else that space curvature may be neglected. We suspect the majority in the community still expect this is true, on the basis of the coincidences argument in Sec. III.B.2, but it will be important to see what comes out of joint fits of both _M0 and ₀, as well as all the other parameters, as is becoming the current practice. Our test-by-test discussion is useful for sorting out the physics and astronomy, we believe; it is not the prototype for the coming generations of precision application of the tests.

Our remarks are ordered by our estimates of the model dependence.

⁶⁷ This was recognized by Zel'dovich (1964), R. Feynman, in 1964, and S. Refsdal, in 1965. Feynman's comments in a colloquium are noted by Gunn (1967). Peebles attended Refsdal's lecture at the International Conference on General Relativity and Gravitation, London, July 1965; Refsdal (1970) mentions the lecture. Back.