Cosmological singularities in Bakry-\'Emery spacetimes

Understand

We consider spacetimes consisting of a manifold with Lorentzian metric and a weight function or scalar field.

• These spacetimes admit a Bakry-\'Emery-Ricci tensor which is a natural generalization of the Ricci tensor.
• We impose an energy condition on the Bakry-\'Emery-Ricci tensor and obtain singularity theorems of a cosmological type, both for zero and for positive cosmological constant.
• That is, we find conditions under which every timelike geodesic is incomplete.