The Nuclear Impact on Cosmology: The $H_0\hbox{-}\Omega$ Diagram

The \HOmega\ diagram is resurrected to dramatically illustrate the nature of the key problems in physical cosmology today and the role that nuclear physics plays in many of them. In particular it is noted that the constraints on \OmegaB\ from big bang nucleosynthesis do not overlap with the constraints on \OmegaVis\ nor have significant overlap with the lower bound on $\Omega$ from cluster studies. The former implies that the bulk of the baryons are dark and the later is the principle argument for non-baryonic dark matter. A comparison with hot x-ray emitting gas in clusters is also made. The lower bound on the age of the universe from globular cluster ages (hydrogen burning in low mass stars) and from nucleocosmochronology also illustrates the Hubble constant requirement $H_0 \le 66 \Hunits$ for $\Omega_0 = 1$\@. It is also noted that high values of $H_0$ ($\sim 80\Hunits$) even more strongly require the presence of non-baryonic dark matter. The lower limit on $H_0$ ($\ge 38\Hunits$) from carbon detonation driven type~Ia supernova constrains long ages and only marginally allows \OmegaB\ to overlap with \OmegaClus. Diagrams of \HOmega\ for $\Lambda_0=0$ and $\Lambda_0\neq 0$ are presented to show that the need for non-baryonic dark matter is independent of $\Lambda$.