 Understanding the evolution of the universe is what cosmology is all about. Up to this point, we've been using the Newtonian equations. For a full picture, we need to use Einstein's general theory of relativity that includes mass energy and pressure. Plus, we need to consider the curvature of spacetime given its mass energy contents. Here's the equation Friedman developed from this starting point. It is quite similar to the Newtonian version with two key differences. First, the mass density is replaced by the energy density, epsilon. And second, the total energy is replaced by the radius of curvature and the curvature constant that equals minus 1, 0, or plus 1, that tells us which metric to use depending on the nature of the curvature. For an isotropic, homogeneous universe, this says we must exist in one of these three possible universes. If it's flat, the universe will expand forever at an ever-decreasing rate. If it's spherical, it is closed and will eventually collapse back in a big crunch. And if it's hyperbolic, it is open and will expand forever at an increasing rate.