A Simple Harmonic Universe

We explore simple but novel bouncing solutions of general relativity
that avoid singularities. These solutions require curvature k=+1, and
are supported by a negative cosmological term and matter with -1 < w <
-1/3. In the case of moderate bounces (where the ratio of the maximal
scale factor a+ to the minimal scale factor a- is ~ 1, the solutions
are shown to be classically stable and cycle through an infinite set
of bounces. For more extreme cases with large a+/a-, the solutions can
still oscillate many times before classical instabilities take them
out of the regime of validity of our approximations. In this regime,
quantum particle production also leads eventually to a departure from
the realm of validity of semiclassical general relativity, likely
yielding a singular crunch. We briefly discuss possible applications
of these models to realistic cosmology.