Hi Yon, on my statement and your question:

Me: "This acceleration profile is quite compatible with the interior solution, in fact a simple Newtonian interior (shell theorem) has precisely the right profile."

You: "Please explain. Do you mean that the mathematical result of the interior solution is precisely right, or do you mean the heuristics are right?"

A better analysis showed my statement to be wrong. I've plotted some more variables on the (now very busy) chart, i.e., proper velocity and proper acceleration of the test galaxy. Neither have the profile expected for either the exterior or the interior dynamics of Newton (or Schwarzschild for that matter). The magnitude of the acceleration drops rather rapidly to zero at D=0, goes only slightly positive and then drops away to zero.

This completely explains the "sudden kink" in the D-proper graph and also the almost linear movement after that, as is also apparent in Davis' figure 3.2.

An interior dynamics is expected to drop to zero more or less like the blue curve, but then to go positive with the same (mirror image) shape, unlike the curve. An exterior solution is expected the have increasing magnitude as distance decreases, in complete contradiction to the blue curve.

So what does this mean? Is it futile to try and do Schwarzschild kinematics in large scale cosmology? I don't know. You decide.

If you want to check the source of the data, download the updated spreadsheet. It has inevitably grown in size to about 1.3 MB in the process of getting data over longer timescales, creating more rows. I suppose VBA Macros will be a better solution, keeping the number of rows down without losing accuracy in the integration loop.

-J