Which part of the stress-energy tensor gravitates?

Understand

We consider the possibility that, in the semiclassical Einstein equation for cosmological spacetimes, gravity is sourced by the amount of stress-energy that is above that of the instantaneous ground state.

• For this possibility to be consistent, the Bianchi identities must continue to hold.
• This is nontrivial because it means that the ground state expectation value of the stress-energy tensor must be covariantly conserved in spite of the fact that the ground state is generally a different state at different times.
• We prove that this consistency condition does hold.