The first part of Table 1 refers to the idea that our universe has expanded from a considerably hotter denser state. Here, as Joe Silk describes in his contribution to these proceedings, we are on reasonably safe ground. Distant objects, whose recession velocities approach the velocity of light, are quite close to isotropic around us. Since distant galaxies seem to be equally good homes for observers the straightforward interpretation is that the universe is close to homogeneous in the large scale average. In a homogeneously expanding universe the recession velocity is proportional to the distance. This is Hubble's law; it is observationally well established. We are in a uniform sea of cosmic background radiation, the CBR, with a spectrum that is quite close to thermal at T = 2.73 K. The only known explanation is relaxation to statistical equilibrium. This could not have happened in the universe as it is now because space is transparent: distant galaxies are observable as radio sources at CBR wavelengths. The inference is that the CBR is a remnant from a time when the universe was denser, hotter, and optically thick. That is, we have direct fossil evidence of the expansion and cooling of the universe.
All these results follow by symmetry arguments with conventional local physics; one does not need the full machinery of general relativity theory. Relativity is probed in more detailed tests.