Transcript: In simple big bang models, that is models without a cosmological constant, the critical density of matter is the density needed to just overcome the expansion so that the universe continues to expand but at an ever decreasing rate. It’s defined mathematically as three times the Hubble constant squared divided by eight times pi times the gravitational constant. Since the critical density is proportional to the Hubble constant squared, this implies that a faster expansion rate requires more matter to overcome the expansion. The value of the critical density given current measurement of the Hubble constant is at about ten to the power minus twenty-eight kilograms per cubic meter. This fantastically small number corresponds to only five hydrogen atoms per cubic meters of space or about one hydrogen atom in the volume occupied by a TV set. The dynamics of the expansion are determined by the matter density of the universe. If the matter density equals the critical density, space is flat, and the universe coasts to a maximum size, taking an infinite amount of time to do so. If the density is less than the critical density, the universe has negative curvature and will expand forever at a decreasing rate or deceleration. If the density is larger than the critical density, the universe will reach a maximum size and re-collapse, and space has a positive curvature. All of these statements are modified in the presence of vacuum energy or a cosmological constant.