1.1. Cosmological Density Parameters
As we have heard at this meeting, there is abundant evidence for the dominance of dark matter and dark energy on the largest distance scales. The cosmological microwave background (CMB) radiation  tells us that the total energy density of the Universe, tot, is very close to the critical value marking the boundary between open and closed universes . This information is provided, in particular, by the value of the multipole ~ 210 at which the first acoustic peak appears in the CMB, as seen in Fig. 1. This tells us, in effect, the relative sizes of the Universe today and when the nuclei and free electrons in the primordial plasma combined to form neutral atoms. There are now indications for a second and even a third acoustic peak in the CMB at higher , but these are not yet securely established. However, the magnitudes of the fluctuations T / T at these larger values of already tell us that the overall baryon density b << 1, agreeing to within ~ 50 % with the value estimated on the basis of Big Bang nucleosynthesis calculations. Other information about the large-scale geometry of the Universe for redshifts z 1 is provided by data on high-z supernovae , which constrain a combination of the matter density m and the vacuum energy density . Combining the CMB and high-z supernova data, one finds fairly accurate values for the cosmological density parameters :
where h is the present-day Hubble expansion rate in units of 100 km/s/Mpc, consistent with the `concordance model': tot ~ 1, / m ~ 2 3 with b small, as seen in Fig. 2. These data may also be used to constrain neutrino degeneracy .
Figure 1. Recent compilation of data on the cosmic microwave background (CMB), exhibiting clearly the first acoustic peak, whose location fixes tot, and the possible second and third peaks at larger .
Figure 2. The combination of cosmological data favours the `concordance' model with tot ~ 1, / m ~ 2 3 and b small, in agreement with cosmological nucleosynthesis .
There are excellent prospects for significant progress in improving the CMB constraints using data from the MAP and Planck satellites . One of the open issues concerns the amount of information likely to be obtained at large , particularly from polarization measurements . These must contend with weak lensing effects that must be subtracted in order to extract useful cosmological information.