Well, as far as GR is concerned, it seems the effects must follow closely. The gravitational field itself moves with the body, and continues to move in a straight line, even if the body has changed directions. Of course, the cause is different. GR is attributed to the warping of space-time, where time and space are actually distorted. With neutrino pressure, the distortion is attributed to the neutrino medium only, where neutrinos are absorbed by a body, and the imbalance of inward and outward neutrino pressures causes another mass to accelerate toward it.

It appears your definition of a vacuum energy density is still identical to that of neutrino pressure as well. The only difference is that it does not predict an expansion or collapse of space-time, but rather that the Hubble constant is created by a loss of energy of light over some distance travelled through the neutrino pressure.

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Let's put together the pieces of The Grand Puzzle . (website - now revised)

"Let's define another operator, Sz, which we won't pay any attention to."
"This transformation will automatically make zero equal zero."
"It may be true that zero equals zero -- and that is certainly an equality -- but I don't want to go into the details at this time."