How does the density of the universe affect its future?
Before 1998 the answer to this question was: if the density is high enough the initial velocity of the Big Bang will be compensated by the gravity due to the mass and the universe will collapse in a Big Crunch. If the density is not enough, the universe will continue the expansion indefinitely.
In 1998 it was discovered that the universe is expanding accelerating. So there is something (we call it dark energy because we do not know what is) that is pushing the galaxies away. Because we do not know how dark energy works, we cannot answer what is the effect of the mass density on the universe. We first need a model for dark energy and then we will have a possible deduction about the evolution.