Within the framework of General Relativity, a universal cosmic time that is relevant for all observers who are commoving with the cosmic substratum can be established by a convenient system of coordinates. However, this is only possible, if the substratum is free from vortices, in accordance with the so-called “Cosmological Principle”. Hence, the existence of a cosmic time depends on contingent properties of the cosmic substratum. – Only if these properties are given, the age and the dynamical behavior of the universe can consistently be described. Under this assumption, we discuss the question, whether the universe could have an infinite past and show that – in spite of a long lasting philosophical debate from Proclus to Kant - there are consistent physical models with infinite age. Furthermore, we argue that the concept of eternity, as it was conceived in the philosophical tradition, can be given an adequate meaning within the context of modern relativistic cosmology. Also this problem can be traced back to ancient Greek philosophy and will be discussed in detail.
Keywords: Cosmic substratum, incoherent matter, cosmological principle, cosmic time, finite past, big bang models, infinite past, Friedmann equation, Eddington-Lema^itre universe, Penrose diagrams, infinitely extended global systems.
