We were asked to debate the value of , the fundamental energy density parameter of cosmology, and in particular its mass component, m. Is the universe flat and marginally bound with m = 1 in accordance with the simplest cosmological model? Is m clearly smaller than unity as seems to be indicated by several observations? Unfortunately, we cannot provide a clear answer at this point because there is conflicting evidence. Entertaining the audience with our biased views on the subject might not be very constructive. Instead, it may be more interesting to lay out the various methods used to measure m, mention new developments and current estimates, and focus on the promising prospects versus the associated difficulties. In the critical discussion that follows we try to shed light on the nature of the uncertainties that may be responsible for the current span of estimates for m.
We divide the methods into the following four classes:
The methods and current estimates are discussed below and summarized in Figure 1 and Table 1. The estimates based on virialized objects typically yield low values of m ~ 0.2 - 0.3. The global measures, large-scale structure and cosmic flows typically indicate higher values of m ~ 0.4 - 1.