Observations indicate that the universe is effectively flat, but they do not
rule out a closed universe. The role of positive curvature is negligible at
late times, but can be crucial in the early universe. In particular, positive
curvature allows for cosmologies that originate as Einstein static universes,
and then inflate and later reheat to a hot big bang era. These cosmologies have
no singularity, no "beginning of time", and no horizon problem. If the initial
radius is chosen to be above the Planck scale, then they also have no quantum
gravity era, and are described by classical general relativity throughout their
history.Comment: minor changes; version to appear in Class Q Gra
