Einstein's theory of general relativity tells us that the curvature of space as a whole is primarily determined by mass, which in turn influences the strength of gravitation. Mass causes space to curve, and this affects the universe's overall geometry. The shape, or curvature, of the universe is determined by the relationship of its actual mass to its critical density, which is the amount of mass necessary to cause the universe to eventually stop expanding. Based on this scenario, there are three possible types of curvature that space could have: flat, positive, or negative.
If the density of the universe is equal to the critical density, then its curvature is zero. It would resemble a sheet of paper spread out in all directions. This is known as a flat or Euclidean universe. The universe would continue its expansion forever, and the expansion would gradually slow down, but it would never stop, because stopping would require an infinite amount of time.
If the density of the universe is greater than the critical density, then it has positive curvature, and its shape would resemble a sphere. The expansion of space would eventually stop and begin to contract. At present, the universe is expanding, and the galaxies are moving away from each other, but in a positive, or closed, universe, they would reach a point where they reverse direction and move closer to each other as the universe collapses.
If the density of the universe is less than the critical density, then this is known as an open universe. Space would be curved somewhat like the surface of a saddle. The amount of matter would be insufficient to stop the universe's expansion, so it would continue to expand forever.
According to NASA, although observations made to date show that the universe could be open, there is insufficient data to form a definitive conclusion. In fact, current theory backed up by recent cutting-edge observations is aligned with the belief that space is geometrically flat.