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:

*Global measures*. Based on properties of space-time that constrain combinations of_{m}and the other cosmological parameters (,*H*_{0},*t*_{0}).*Virialized Systems*. Methods based on nonlinear dynamics within galaxies and clusters on comoving scales 1 - 10*h*^{-1}*Mpc*.*Large-scale structure*. Measurements based on mildly-nonlinear gravitational dynamics of fluctuations on scales 10 - 100*h*^{-1}*Mpc*of superclusters and voids, in particular*cosmic flows*.*Growth rate of fluctuations*. Comparisons of present day structure with fluctuations at the last scattering of the cosmic microwave background (CMB) or with high redshift objects of the young universe.

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.