Cosmological Parameters (4)
Inflationary models (1979-81)
Alexei Starobinsky and Alan Guth proposed models, subsequently improved by Andrei Linde and by Andreas Albrecht & Paul Steinhardt, which assumed the universe went through an enormous expansion very early in its history. A consequence of the theory is that the universe is flat with k = 0, which requires that Ωm + ΩΛ = 1 , where now ΩΛ is associated with the energy density of the vacuum and often referred to as dark energy.
By the late 1990s most cosmologists accepted this.
The present (2003-04)
Today cosmologists try to determine not only k, Ωm, and ΩΛ, but also the age of the universe and the portions of Ωm due to various types of matter, such as baryonic matter, cold dark matter, and hot dark matter. They also would like an independent determination of the age of the Universe and the time that elapsed between the Big Bang and recombination, when atoms formed and the Universe became transparent. Amazingly, analysis of the anisotropies in the CMB, provides values for all of these and more.
Max Tegmark, et al (67 authors) attempt to determine all of the cosmological parameters based on analysis of results of WMAP, the Sloan Digital Sky Survey, and other data in a really, really difficult paper last revised in early 2004. If you can read this, you are far above Astronomy 350! There is a simplified summary on the SDSS website.
Note: There is nothing at all critical about the critical density if the cosmological constant is not zero, but the term is still used.
Cosmological Parameters:  1 2 3 4