The classical singularity theorems of R. Penrose and S. Hawking from the
1960s show that, given a pointwise energy condition (and some causality as well
as initial assumptions), spacetimes cannot be geodesically complete. Despite
their great success, the theorems leave room for physically relevant
improvements, especially regarding the classical energy conditions as
essentially any quantum field theory necessarily violates them. While
singularity theorems with weakened energy conditions exist for worldline
integral bounds, so called worldvolume bounds are in some cases more applicable
than the worldline ones, such as the case of some massive free fields. In this
paper we study integral Ricci curvature bounds based on worldvolume quantum
strong energy inequalities. Under the additional assumption of a – potentially
very negative – global timelike Ricci curvature bound, a Hawking type
singularity theorem is proven. Finally, we apply the theorem to a cosmological
scenario proving past geodesic incompleteness in cases where the worldline
theorem was inconclusive.
