What does the omega sign mean in physics and cosmology?

Omega is the ratio of the density of the universe to the critical density.
The density of the universe is the amount of matter per unit volume averaged for the entire universe. The critical density is the average density of matter required for the universe to just halt its expansion but only after infinite time.
Omega at the current time is measured as ##1.02 +- 0.02## indicating that the universe is very close to the critical density (or ## =1##).
The critical density is calculated to be ##9.47 xx 10^(-27) kgm^(-3)##. Of this critical density ordinary matter (baryonic matter) is thought to make up only about 4% with dark matter contributing 23% and dark energy providing the remaining 73%.
The relation between the actual density and the critical density determines the overall geometry of the universe. If both are equal the geometry (Euclidean) of the universe is flat. It expands forever but has a speed that slowly approaches zero.