Applications
Distributions of negative energy density comprise what is often referred to as exotic matter, and allow for several intrgiuing possibilities: for example, the Alcubierre drive potentially allows for faster-than-light space travel.
Quantum inequalities constrain the magnitude and space-time extent of negative energy densities. In the case of the Alcubierre warp drive mentioned above, the quantum inequalities predict that the amount of exotic matter required to create and sustain the warp drive "bubble" far exceeds the total mass-energy of the universe.
Read more about this topic: Quantum Inequalities