The curvature of the universe is determined by the density of the universe. You can do a cosmic inventory of all of the mass from ordinary matter in a representative region of the universe to see if the region's density is above the critical density. Such an inventory gives 10 to 20 times too little mass to close the universe. The primordial deuterium abundance provides a sensitive test of the density of ordinary matter in the early universe. Again, you get 5 to 15 times too little mass to close the universe. However, these measurements do not take into account all of the dark matter known to exist. Dark matter is all of the extra material that does not produce any light, but whose presence is detected by its significant gravitational effects.