Does quantum field theory enforce the averaged weak energy condition?

Abstract

The renormalized expectation value of a quantum stress-energy tensor generally violates the local positive-energy conditions of general relativity. It has been recently discovered that the averaged weak energy condition, which requires the positivity of energy only when suitably averaged along null geodesics, is satisfied in all quantum states of any scalar quantum field theory on Minkowski spacetime. The author shows that this averaged energy condition also holds on an arbitrarily curved two-dimensional background for a conformally-coupled scalar field, provided the background spacetime satisfies certain asymptotic regularity requirements. These results raise the intriguing possibility that the averaged weak energy condition might hold quite generally for quantum field theory in a four-dimensional asymptotically flat spacetime.