Geodesically complete universes

TL;DR

This paper classifies all possible non-singular, continuous, and globally hyperbolic extensions of FLRW cosmologies into three main types, revealing a highly restricted set of viable models consistent with quantum gravity considerations.

Contribution

It systematically extends previous studies by analyzing all potential non-singular past extensions of FLRW universes, identifying only three feasible cosmological scenarios under homogeneity and isotropy.

Findings

Identifies three non-singular cosmological models: bouncing, emergent, and asymptotically emergent universes.

Shows that homogeneity and isotropy severely limit viable non-singular extensions.

Discusses implications for initial conditions and the arrow of time in cosmology.

Abstract

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.