Eternal universes

We consider the possibility of a past and future eternal universe, constructing geodesically complete inflating, loitering, and bouncing spacetimes. We identify the constraints energy conditions that general relativity place on the building of eternal cosmological models. Inflationary and bouncing behavior are shown to be essential ingredients in all significant examples. Nontrivial complete spacetimes are shown to violate the null energy condition for at least some amount of time, as well as the average null energy condition, unless curvature is included. Ignoring the intractable subtleties introduced by quantum considerations, such as rare tunneling events and Boltzmann brains, we demonstrate that these universes need not have had a beginning or an end.