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The boundary density between the case where the universe has enough mass/volume to close universe and too little mass/volume to stop the expansion is called the critical density. The critical density = 3H2/(8pG), where H is the Hubble constant for a given cosmological time. Notice that the Hubble constant has appeared again! It measures the expansion rate, so it should be in the critical density relation. The current critical density is approximately 1.06 × 10-29 g/cm3. This amounts to six hydrogen atoms per cubic meter on average overall.
A critical density universe has ``flat'' curvature. The W density parameter equals exactly 1 in a flat universe. The Hubble ``constant'' is not really a constant—it is different at different cosmological times. The greater the value of the Hubble constant at a given cosmological time, the faster the universe is expanding at that time. Gravity slows the expansion of the universe, so the early universe was expanding faster than it is now. That means that the critical density was greater at earlier times. It changes by the same factor that the actual density of the universe changes throughout the expansion. So if the universe starts out with a density greater than the critical density, then its density will always be greater than critical density. If the universe starts out with a density less than the critical density, then its density will always be less than the critical density.