Is vacuum acceleration directly proportional to distance?

[69911e]

Do we know if the instantaneous/observed acceleration due to the vacuum is directly proportional to distance or possibly? (ignore any gravitational effects)
A~D ?
A~D^2 ?
A~D^(1/2) ?
A~D^(-2)
A~D^(Other) ?
OR
A= constant (edited as I forgot this one)

If not, is there a best guess/fit or simply not precise enough data?

Feel free to correct my question if it is simply a bad question. I didn't see this directly address in any thread; if I missed one, a link would be great.

 

[PeterDonis]

the instantaneous/observed acceleration due to the vacuum

What do you mean by this?

 

[69911e]

What do you mean by this?

The observed acceleration of distant objects from the supernova data or other observation.

 

[marcus]

Do we know if the instantaneous/observed acceleration due to the vacuum is directly proportional to distance or possibly? ... if I missed one, a link would be great.

You could look at the Hypersine thread.

To an excellent approximation, distances are growing and are expected to continue growing as the function
sinh^2/3(1.5 t) where the present is at time t = 0.8

This looks more and more like exponential growth (at a very low rate of about 1/173 % per million years) as time goes on. Eventually it will be indistinguishable from exponential growth at that rate call it H_∞

D(t) = e^H_∞t

If you differentiate that you get the expansion speed is proportional to the distance multiplied by H_∞ and if you take the derivative again you get the acceleration is proportional to the distance multiplied by the square of H_∞

The Hypersine thread https://www.physicsforums.com/threads/the-hypersine-cosmic-model.819954/#post-5146660
has some graphs that show the distance growth curve and the gradual onset of exponential growth at a small constant rate.

 

[69911e]

The Hypersine thread provided the understanding of the acceleration rate I was looking for.
Thanks!