Nereid said:
Sorry, it seems I wasn't clear turbo-1.
The 120 OOM is a big elephant, no doubt.
What I was asking was what - quantitatively (or even with equations without estimated parameters!) - do we have to link the ZPE (or similar) to the estimated non-baryonic DM we 'see' in rich clusters?
Yes, but I do not have the math skills to make the all the field calculations. To get an estimate of the gravitational energy of the polarized vacuum field one could simply give it the gravitational attraction attributed now to non-baryonic DM (perhaps less some fraction for unobserved baryonic DM).
Here come the tricky parts:
a) How does the attractive force in the polarized vacuum scale with distance? Does it fall of as a function of the square of the distance from the dominant mass? This seems problematic in light of the self-attractive self-polarizing nature of the vacuum field, and may be the root cause of the disagreement between GR and MOND on galactic scales.
b) On galactic scales, it is apparent that the GR approximation results in a mass shortfall (as expected by the rotation curves of spirals in particular). MOND is reasonably predictive on galactic scales, but does not perform as well in clusters. This leads to another part of the model that I have not yet refined to my satisfaction. If we model a polarized vacuum field surrounding an isolated elliptical, we will probably end up with a field shape that mirrors the mass distribution of the galaxy. Add a second galaxy nearby, and what happens? Where their fields overlap, they will by necessity distort as they merge, perhaps forming a field that in total looks like a large blob with a central "pinch" or some other morphological version of a dogbone. I expect that the "pinch" will be pronounced when the galaxies are relatively distant from one another and much less pronounced when they are very close, resembling an ellipsoid with very soft lobes. The virtual particle pairs near this overlap will be strongly influence by the orientation of their neighbors, and will have to come to some equilibrium irrespective of the location of the masses that generated the polarized fields.
c) OK, the determining the shape of the combined fields of two galaxies is not trivial. How now to model the shape and density of the cluster's vacuum field when there are multiple galaxies of various masses and shapes, each with its own momentum? At this point, it's clearly supercomputer time, but I imagine the final picture will look like a filamentous structure with lobes surrounding each galaxy or close grouping.
Sorry about the delay in answering you, Nereid. Your questions are good, and I wish I could be more quantitative. I've got the basics of the model pretty firmly established, but the morphology of the galactic/cluster fields gets complicated, and I have not been as diligent in thinking these through, although modeling strong cluster lensing in terms of classical optics was a prime motivation for heading down this ZPE field path in the first place.