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The classical singularity theorems of R. Penrose and S. Hawking from the1960s show that, given a pointwise energy condition (and some causality as wellas initial assumptions), spacetimes cannot be geodesically complete. Despitetheir great success, the theorems leave room for physically relevantimprovements, especially regarding the classical energy conditions asessentially any quantum field theory necessarily violates them. Whilesingularity theorems with weakened energy conditions exist for worldlineintegral bounds, so called worldvolume bounds are in some cases more applicablethan the worldline ones, such as the case of some massive free fields. In thispaper we study integral Ricci curvature bounds based on worldvolume quantumstrong energy inequalities. Under the additional assumption of a - potentiallyvery negative - global timelike Ricci curvature bound, a Hawking typesingularity theorem is proven. Finally, we apply the theorem to a cosmologicalscenario proving past geodesic incompleteness in cases where the worldlinetheorem was inconclusive.

Hawking-type singularity theorems for worldvolume energy inequalities