In this paper, it is proposed that the correct metric for relativistic cosmology is one which has not only spatial curvature, but time curvature as well, and that it is the curvature of the time dimension that is the source of the accelerated expansion. It is argued that the FRW metric, whose time dimension is uncurved, is effectively a Newtonian approximation to the true cosmological metric and that the internal Schwarzschild metric is the true cosmological metric describing the 3D space of the Universe falling through the time dimension. The unknowns in the internal Schwarzschild metric are solved for using cosmological data and it is shown that the predictions it gives match observations without the need for a cosmological constant. The entire Schwarzschild metric in Kruskal-Sezekeres coordinates is examined and we see that it describes two CPT symmetric Universes moving in opposite directions in the time dimension. One Universe contains matter while the other contains antimatter. It is then shown that due to the sign of the angular term in the internal Schwarzschild metric, the time dimension is the imaginary counterpart of the spatial dimension in the external metric. At the singularity, the geodesics reverse their direction in time and begin to re-collapse toward each other. The matter and antimatter Universes annihilate with each other when they collide at the end of collapse, ultimately decaying into two new matter and antimatter Universes. Finally, we look at the external Schwarzschild solution and find that gravitational event horizons cannot be formed or reached until the end of the re-collapse. We find that all the gravitational event horizons in the Universe represent the same point which is the annihilation event at the end of re-collapse.