  The Borde-Guth-Vilenkin (BGV) theorem states that any spacetime with net
positive expansion must be geodesically incomplete. We derive a new version of
the theorem using the fluid flow formalism of General Relativity. The theorem
is purely kinematic, depending on the local expansion properties of geodesics,
and makes no assumptions about energy conditions. We discuss the physical
interpretation of this result in terms of coordinate patches on de Sitter
space, and apply the theorem to Penrose's model of Conformal Cyclic Cosmology.
We argue that the Conformal Cyclic extension of an asymptotically de Sitter
universe is geodesically incomplete.
