On Singularities in Cosmic Inflation

TL;DR

This paper demonstrates that all flat FLRW cosmological models with scalar fields inevitably develop finite-time singularities, challenging assumptions about the smoothness and predictability of inflationary scenarios.

Contribution

It applies Osgood's criterion to Einstein's equations, revealing that solutions in inflationary models generically become singular in finite time, regardless of potential choice.

Findings

All models develop finite-time singularities

Solutions lack global existence and uniqueness

Implications for the role of inflation in cosmology

Abstract

In this paper, we examine a flat FLRW spacetime with a scalar field potential and show by applying Osgood's criterion to the Einstein field equations that all such models, irrespective of the particular choice of potential develop finite-time singularities. That is, we show that solutions to the field equations become singular in finite time, which can have important implications for the role of inflation in cosmological models. We further point out that a possible reason for this behaviour is that the solutions to the field equations in such inflationary scenarios do not obey global existence and uniqueness properties, which is a typical characteristic of solutions that diverge in finite time.