Hi Jon, you wrote:

"Now you will argue that, from the galaxy's perspective, the origin's proper recession velocity away from it will decrease over time, as a result of the cosmic gravitational deceleration. (The obvious fallacy is that in your model gravity imparts acceleration to the dust but not to a galaxy moving through the dust)."

Where did you get the idea of the "fallacy"? In the hypersphere model, the momentums are present in the hyperspherical direction only for comoving particles and in both spatial and hyperspherical directions for particles with peculiar motion.

Your: " Let's do you one better and run a case where the origin's recession velocity drops to zero instantly upon the untethering. Then, at a proper velocity of 71 km/s toward the stationary origin, the unaccelerated galaxy would require 6.95E+13 years to reach the origin, that is, 69,500 GY. "

The "… origin's recession velocity drops to zero instantly upon the untethering" means that the whole hyperspherical motion da/dt is instantly changed to da/dt=0. This action imparts one huge, instant acceleration shock to all particles and will cause the untethered particle to acquire a huge negative proper velocity component. The broad idea is pictured (left) in the form of a portion of hypersphere, presented in one space and one hyperspace dimension. I just modified a picture from my eBook, so some information in black are superfluous.

χ is the comoving distance parameter and χR the proper distance of the tethered galaxy, where R is radius of curvature.

The observer and the distant object follow the red dotted hyperspace paths as scale factor a increases. While still tethered, the test galaxy follows the dotted blue path, at constant χR. The shock must obviously stop the observer and distant object in their hyperspace tracks and can be viewed as a hypervelocity change as indicated by the solid red vectors. The shock will however impart the same hypervelocity change to the test galaxy and will give it a huge negative proper velocity (solid blue vector), due to its peculiar hyperspace path when tethered.

There are many ways to describe this, but I prefer it in relation to the hypersphere model, because I can plot and visualize it for any expansion profile over time. If scale factor a increases as per the matter only (1,0) case, the deceleration of a_dot can be viewed as continuously imparting small shocks to the hypersphere and hence continuously accelerating the test galaxy towards the origin. This is just a more formal way of describing what I loosely stated in 3.1 to 3.6 of post #59.

This does mean that there is a form of proper acceleration working on the untethered galaxy, coming from large scale changes in expansion rate, not from a local Schwarzschild type of gravitational acceleration effect. I think this is at the core of our disagreement. I offer again: show me rigorously how such a local Schwarzschild gravity can produce the acceleration profiles, and I'll concede the point (at least halfway ).

-J