 Cosmological theory has gone through many phases and proposals over the past 100 years. Some have included universes with infinite pasts and these were mentioned previously. However, for the past forty years there has been a strong consensus on the modern big bang theory which has a finite past. But even if the universe is temporally finite in the past, it may well be spatially and materially infinite. If space is infinite and the cosmological principle is assumed to be valid, the universe will contain an infinite number of galaxies, stars, atoms and everything else. Such actual infinities not only cause philosophical and logical problems, they may also cause problems of a theological nature. In his thought experiment known as “Hilbert’s hotel” the famous mathematician David Hilbert argued that (countable) actual infinities are so bizarre that they cannot have anything to do with the real world we live in. In this thought experiment, Hilbert imagines that he arrives at a hotel with an infinite number of rooms, all of which are occupied. The desk clerk claims nonetheless that there is a vacancy. He then proceeds to ask each guest to move to the room with the next highest number in the sequence (see Oppy 2006, 8; Kragh 2014, Other Internet Resources).