General relativistic cosmology with no beginning of time
  We find that general relativity can be naturally free of cosmological singularities. Several nonsingular models are currently available that either assume ad hoc matter contents, or are nonsingular only over a sector of solution space of zero measure, or depart drastically from general relativity at high energies. After much uncertainty over whether cosmological inflation could help solve the initial-singularity problem, the prevailing belief today is that general relativistic cosmology, with inflation or without, is endemically singular. This belief was reinforced by recent singularity theorems that take account specifically of inflation. Here, a viable inflationary cosmology is worked out that is naturally free of singularities despite the fact that 1) it uses only classical general relativity, 2) it assumes only the most generic inflationary matter contents, and 3) it is a theory of the chaotic-inflation type. That type of inflation is the most widely accepted today, as it demands the least fine-tuning of initial conditions. It is also shown how, by dropping the usual simplification of minimal coupling between matter and geometry, the null energy condition can be violated and the relevant singularity theorems circumvented. 
Redouane Fakir