Moving objects in retarded gravitational potentials of an expanding spherical shell/Conclusion

Conclusion
The considerations described above show that retarded gravitational potentials can contribute to the explanation of the accelerated expansion of the visible part of the universe, if the outer spherical black shell of the universe would consist of expanding dark matter with a huge mass. However, this would also hold in a steady state universe and even if the outer dark shell of the universe would not move at all. But in the latter case any moving mass in that shell would reach the shell in a finite time.

It can also be considered that the effect of the retarded gravitational potentials will accelerate moving objects the more, the faster they move, and therefore, the closer they are to the spherical shell of dark matter. Furthermore, also objects within smaller spherical shells that not only are surrounded by dark matter, but also by visible objects will experience the retarded gravitational potentials of these objects, and therefore, will experience an additional acceleration which is directed outwards.

Computing the corresponding and permanently increasing Schwarzschild distances results in two remarkable points in time where we today can observe the cosmic microwave background at a cosmic age of 380,000 years as well as the most distant known galaxy at a cosmic age of 290 million years. Cosmologists call the period in between as the dark ages, where dark matter was massively transformed into "dark energy". So far, the nature of "dark energy" is unclear, but the invisible black shell at the outer rim of our universe could contribute to find an explanation.

Due to Newton's third law (actio = reactio) the shell experiences the same retarded gravitational forces as the moving masses within the shell. These forces will cause a deceleration of the shell which is the stronger the closer the masses within the shell are to it.

The high velocity of visible objects near the outer dark rim of the universe as well as the huge mass of the dark matter in front of them seem to be the reason for the extreme redshift of their light that can be observed. The observation that this redshift is greater than expected for distant objects led to the assumption that the further away these objects are, the more they are accelerated. Another reason for this could be found in the effects of the retarded gravitational potentials of a massive dark outer shell. Furthermore, the additional gravitational redshift leads to a higher value than expected only by the relativistic Doppler effect. This is in accordance with the observations of very far and young galaxies such as JADES-GS-z14-0 or of the cosmic microwave background (CMB).

However, the computation of the accelerations of moving objects due to retarded gravitational forces becomes extremely expensive, if the outer shell is neither homogeneous, nor spherical or symmetrical. Furthermore, relativistic effects (including the transverse Doppler effect) could cause time dilatation or mass increase that would have to be considered, too. Finally, is would be necessary to consider the loss of mass in the visible universe over the time, since a significant amount of visible matter may have traversed the event horizon that is caused by the huge mass of the outer shell of the universe.