Energy density can be negative according to quantum theory.

Evidence

In other words, quantum theory allows the energy density to be negative in some places, provided that this is made up for by positive energy densities in other places, so that the total energy remains positive. — Hawking, Stephen, A Brief History of Time, 290

Categorization

• corroborated: 2 independent passages support this claim — Hawking, Stephen, A Brief History of Time, 290