  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.
