  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.
