Michael Noonan asked if this was a new geometry. No, it is not. A new geometry requires a mathematical framework, which is lacking. It might be that a mathematical framework for this model would involve a new geometry, but I doubt it.

I am sorry I do not understand the question, “is this still 3D 1 time and 1 inner 4d inflation with dark energy and matter…”. Actually, the model I have described is close to Euclidian, but takes special relativity into account. I realize that is terrible for a description of a model, because our universe is definitely not Euclidian. Oh, yes, there is some acknowledgement of another geometry at work here, for example, at the high velocities required by the models, the mass of the stars and galaxies at great distances would increase. The Euclidian model does allow for simpler math, however.

Dark matter actually is not concretely addressed in the model, just by speculation. If gravity increasing over current models with distance happens to be observable at the galactic level, then the expectation would be that the increased gravity would cause faster rotations around the center of the galaxy. Faster rotations around the center of galaxies have been observed by red and blue shifts, and the explanation which has been given for this in the past has been the presence of dark matter. Some, maybe even all of the faster rotation might be explained by more gravity at greater distances than what current models reflect.

I agree that it would be great to have some mathematics to go with the model, but what I would have to offer is elementary and very well-known, and the actual math for the model would need to be built on observations. So the math has not been constructed to reflect the model. I can, however, provide some of the math necessary to build the chart for the gravity and distance from the center of gravity.

Start with a chart which shows the amount of red shift vs. distance from Earth. The spectrum lines show the amount of the red shift, and thus, the frequency for different spectrum lines can be known. From special relativity, when a red shift is due exclusively to transverse Doppler and the velocity is known, the ratio for the red shift is

C/√(C²-V²) = frequency of sun / frequency of star

Let su be used to represent the frequency of the sun
Let st be used to represent the frequency of the star or galaxy

c = (SU/ST)*√(C²-V²)
C/(su/st) = √(C²-V²)
(C*st/su)² = C²-V²
v = √(C²-((c*st/su)²))

Thus, the velocity can be determined, if it is due 100% to transverse Doppler. From there, a chart can be built showing the velocity of the galaxies vs. the distance from Earth.

Knowing the velocity, it is possible to determine the gravitational attraction, assuming the galaxy is in a circular orbit around the center of gravity for the universe, with Earth being near that center. Sorry, I do not know the equations for this.

After the chart has been built, there will be a huge gap for distances closer to the Earth. We can arrive at a range of values, but perhaps no great accuracy for these closer distances by attributing some of the faster rotation around the center of galaxies to be due to increasing gravity. How much of that should be attributed to increasing gravity and how much to the presence of dark matter? I do not know.

Also, in building the chart, take into account the slow-down in our spacecraft as they leave our solar system, along with the margin of error. We do not know if there are other explanations for the slow-down other than increasing gravity.

It is also important to show how the model could be discredited or gain credibility.

One of the challenges in discrediting the model is the inherent flexibility of the model. Since the model is based on the concept that gravity is different at a great distance, are there any other laws that could be different, such as time, with distance from the center of gravity of the universe? It might be that at some point, too many laws have to be bent too far that the model could become unacceptable to even its strongest advocates.

It seems to me that it is very difficult to disprove the model, but just because it is difficult to disprove it does not make it right. I know there are others who might have better ideas than I have on this, but I would like to give my thoughts.

It is possible to measure the velocity of a wide variety of stars and galaxies at different distances, based on this model, but even if a wide variety of pairs of galaxies could be measured, and the distance between them could be shown not to change over time, it simply could be argued that a pair was picked which happen to be traveling in the same direction.

It is not possible, with this model, the universe being spherical, for all the galaxies to be traveling in the same direction at every point and still have a fairly even distribution of galaxies at all distances and directions from the center of gravity for the universe. The high velocity of these galaxies should make it easier to detect when galaxies are traveling closer together or further apart.

I suppose that without exhaustive surveys, not being able to detect galaxies which are traveling closer together or further apart at great distances from us would not disprove the model. However, if a pair of galaxies were found at a great distance from us to be moving together or apart at great speeds, more compatible with this model than the big bang model that would tend to credit this model and discredit the big bang theory.

Another way is look at a distant star in a distant galaxy though a gravitational lens. A galaxy will not work. Maybe two gravitational lenses perfectly aligned would work. Account for any distortions in the lens itself. Is the resolution strong enough to measure the dimensions of the star? Is the star far enough way and the lens accurate enough (not too distorted)? Is the star shorter in one direction than in another direction? If, under these conditions, and within the margin of error, the dimensions are the same in all directions, then that would discredit this model and tend to confirm an expanding universe. On the other hand, if the star shows it is longer in one direction than another, shaped like a football, that would tend to confirm this model and discredit an expanding universe. The ratio of the lengths can be used as another measurement of the velocity, and it can be determined if that measurement of the velocity coincides with the measurement based on the red shift under this model.

Are there simpler observations at closer distances that could help? The best I could suggest would be dicey and hypothetical and with too wide a margin of error. See if our spacecraft continue to decelerate as they leave us. Can we account for the deceleration by other mechanisms? Decide how much of the faster rotation around galaxies can be attributed to dark matter and how much could be attributed to increasing gravity, as if it actually is our prerogative to make such a decision.

Others more knowledgeable than I may come up with other suggestions on how to test the model.