General Relativistic Cosmology with No Beginning of Time

We find that general relativity can be naturally free of cosmologicalsingularities. Several nonsingular models are currently available that eitherassume ad hoc matter contents, or are nonsingular only over a sector ofsolution space of zero measure, or depart drastically from general relativityat high energies. After much uncertainty over whether cosmological inflationcould help solve the initial-singularity problem, the prevailing belief todayis that general relativistic cosmology, with inflation or without, isendemically singular. This belief was reinforced by recent singularity theoremsthat take account specifically of inflation. Here, a viable inflationarycosmology is worked out that is naturally free of singularities despite thefact that 1) it uses only classical general relativity, 2) it assumes only themost generic inflationary matter contents, and 3) it is a theory of thechaotic-inflation type. That type of inflation is the most widely acceptedtoday, as it demands the least fine-tuning of initial conditions. It is alsoshown how, by dropping the usual simplification of minimal coupling betweenmatter and geometry, the null energy condition can be violated and the relevantsingularity theorems circumvented.