I want you to show, mathematically, that it follows that if ADG is constant inside an object, curvature and expansion are the same (or vice versa).
I can not definitive prove mathematical it is the same, because what you then ask me about is mathematically to prove that space inside for example the Earth is stretching.
Remember that the basic claim of GR is that space “bends”.
This is off course not 100 % proven, but still we all understand that this is
a "indisputable mathematical fact".
Also even though we even do not understand what "bends" really mean.
The reason for this is that several consequences fit with the predicted model.
I to can (indirectly) predict several consequences, and have already done so.
Indirectly I can predict that ADG 1 mm from the centre of a body will be the same at the surface inside a (homogenous) mass.
If this is correct it first at all force you to accept that this prediction
only was possible based on the understanding and as a consequence of that that “the of curvature of space” means = stretching space.
In this context, remember that math is already available to demonstrate exactly that fact, all what is left is
to understand the deeper meaning of that math.
For example it is known that when radius away from a body doubles, ADG is decreasing 75%.
This is proportional to that also the square increase is 75 %, - which logical shows that ADG depend of the “access to space”, - and hence this a mathematical language that already shows that space is consumed / affected proportional with the “access” to open space..
In no other way gravity can in fact reach infinity.
But off course I must admit that there will always be people that do not want to accept even overwhelming logic and coherent facts.
It has no already been done, so far as I'm aware. If it has been, give me a reference. Where did you read that?
I mean it is already known how time and curved space is related (space-time).
It’s just to continue on that track, because this also comprehends the expanding space, in the exact same way.
If a distance (the meter stick) expands with factor 2, time too stretch with the same factor, and ticks slower.
It is inevitable that a deeper understanding of gravity
mustunite gravity and the expanding space. I am imaging that I will assemble the first 10 pieces to that puzzle and prove that these fits, then plenty others will show that there is 100 more pieces that also fits.
The “curvature of space” and the “expanding space” can’t be opposite “forces” that counteracts each other; - This idea is in no way proven or even logic. .
The first place the new acknowledgment must strike is that the expanding universe not can be ignored of gravity forces.
This off course means that the (relative) distances for example between the Sun and the planets must change over time
This is the time the prevailing foundation automatically cracks and indisputable forces us to rethink the whole mathematical foundation and understanding as well.