C. The state of the cosmological tests

Precision cosmology is not very interesting if it is based on faulty physics or astronomy. That is why we have emphasized the tests of the standard gravity physics and structure formation model, and the checks of consistency of measures based on different aspects of the astronomy.

There are now five main lines of evidence that significantly constrain the value of _M0 to the range of Eq. (59): the redshift-magnitude relation (test [4]), gravitational dynamics and weak lensing (test [7]), the baryon mass fraction in clusters of galaxies (test [8]), the abundance of clusters as a function of mass and redshift (test [9]), and the large-scale galaxy distribution (test [12]). There are indications for larger values of _M0, from analyses of the rate of strong lensing of quasars by foreground galaxies (test [6]) and some analyses of large-scale flows (test [7]), though we know of no well-developed line of evidence that points to the Einstein-de Sitter value _M0 = 1. Each of these measures of _M0 may suffer from systematic errors: we must bear in mind the tantalus principle mentioned in Sec. I.A, and we have to remember that the interpretations could be corrupted by a failure of standard physics. But the general pattern of results from a considerable variety of independent approaches seems so close to consistent as to be persuasive. Thus we conclude that there is a well-checked scientific case for the proposition that the measures of the mean mass density of matter in forms capable of clustering are physically meaningful, and that the mass density parameter almost certainly is in the range 0.15 _M0 0.4.

In the standard cosmology the masses of the galaxies are dominated by dark matter, with mass density parameter _DM0 ~ 0.2, that is not baryonic (or acts that way). We do not have the direct evidence of a laboratory detection; this is based on two indirect lines of argument. First, the successful model for the origin of the light elements (test [2]) requires baryon density _B0 ~ 0.05. It is difficult to see how to reconcile a mass density this small with the mass estimates from dynamics and lensing; the hypothesis that _M0 is dominated by matter that is not baryonic allows us to account for the difference. Second, the nonbaryonic matter allows us to reconcile the theory of the anisotropy of the cosmic microwave background radiation with the distributions of galaxies and groups and clusters of galaxies, and the presence of galaxies at z ~ 3 (tests [11] and [12]). This interpretation requires a value for _B0 that is in line with test (2). The consistency is impressive. But the case is not yet as convincing as the larger network of evidence that _M0 is well below unity.

The subject of this review is Einstein's cosmological constant , or its equivalent in dark energy. The evidence for detection of by the redshift-magnitude relation for type Ia supernovae is checked by the angular distribution of the 3 K cosmic microwave background temperature together with the constraints on _M0. This certainly makes a serious case for dark energy. But we keep accounts by the number of significant independent checks, and by this reckoning the case is not yet as strong as for nonbaryonic dark matter.