TL;DR
This paper proposes a class of inflationary cosmological models that originate from a static universe, avoiding singularities and the need for quantum gravity, while explaining the universe's flatness and inflation.
Contribution
It introduces a non-singular inflationary cosmology based on positive curvature allowing a universe to start as an Einstein static universe and evolve without a quantum gravity era.
Findings
Models have no initial singularity or horizon problem.
Universe can originate from a static state and inflate without quantum gravity.
Initial radius above Planck scale avoids quantum gravity era.
Abstract
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.
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