  Singularity theorems demonstrate the inevitable breakdown of the concept of
continuous, classical spacetime under highly general conditions. Quantum
gravity is expected to intervene to avoid singularities and models so far hint
towards several regularized geometries, in which limited spacetime regions
requiring full quantum gravitational description can be safely covered by an
extension of some suitable spacetime geometry. Motivated by these premises, in
recent years, a systematic, quantum gravity agnostic, study has been carried
out to catalogue all the conceivable non-singular, continuous, and globally
hyperbolic geometries arising from evading Penrose's focusing theorem in
gravitational collapse. In this study, we extend this inquiry by systematically
examining all potential non-singular, continuous, and globally hyperbolic
extensions into the past of Friedmann-Lema\^itre-Robertson-Walker (FLRW)
metrics. As in the black hole case, our investigation reveals a remarkably
limited set of alternative scenarios. The stringent requisites of homogeneity
and isotropy drastically restrict the viable singularity-free geometries to
merely three discernible non-singular cosmological spacetimes: a bouncing
universe (where the scale factor reaches a minimum in the past before
re-expanding), an emergent universe (where the scale factor reaches and
maintains a constant value in the past), and an asymptotically emergent
universe (where the scale factor diminishes continually, asymptotically
approaching a constant value in the past). We also discuss the implications of
these findings for the initial conditions of our universe, and the arrow of
time.
