The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity. They were first derived by Alexander Friedmann in 1922 from Einstein’s field equations of gravitation for the Friedmann-Lemaître-Robertson-Walker metric and a fluid with a given mass density and pressure . The equations for negative spatial curvature were given by Friedmann in 1924.
From the Friedmann equation, we can model the development of the universe as time progresses. With advances in the our understanding of the cosmological constant k (read, dark energy) and cosmic microwave background radiation anisotropies we have come to the conclusion that we live in a universe that is not only expanding, but that it is accelerating. Whether or not the acceleration of the universe will continue to increase or start decelerating is unknown However, based on our current understanding of the universe, we know that mass and pressure density will continue to decrease as the universe expands, whilst dark energy will increasingly dominate. With that in mind, if dark energy continues along its current trend, that it is reasonable to assume that our universe will expand forever.