Certain of those assumptions seem reasonably sound. The idea that the Law of Gravitation applies equally everywhere in the Universe seems reasonable. The idea that the speed of light and other known constants such as PI and e and h are invariable also seem logical.
However, there is a well known phenomenon that might make certain of these constants appear as though they might have slightly different values. It is called the Compton Effect. It is well documented that there are some experiments where a photon interacts with an electron, and manages to impart some kinetic energy to the electron. The photon that then leaves the area has less total energy, which means that it is redder in color than before it interacted with the electron.
Virtually all objects that astrophysics believes to be very distant, have very large red shifts. The standard understanding of this red shift is that it is entirely due to the Doppler Effect, where a light source that is moving away from us has fewer wavefronts getting to us each second, which therefore also causes a red shift. The Doppler Shift is so universally accepted as the cause of the red shift seen in all distant object that the phrases "Red Shift" and "Doppler Shift" are often used almost interchangeably.
The point of this essay is to suggest that there are a number of other possible sources for a red shift seen in stars' spectra. Something like the Compton Effect is worthy of consideration. So are other possibilities.
The general premise is that, in a light path that might be billions of light-years long, a lot of unrecognized things might happen! In empty space, there are not a lot of atoms and electrons, but in a path-length of billions of light years long, a photon might happen to encounter one. If it's interaction with an electron was such that a Compton Effect occurred, the continuing photon would have less energy, and therefore appear to be red-shifted.
In the case of the Compton Effect, it would be tough to present a persuasive argument though, regarding galactic red shifts. A Compton Effect encounter involves a single photon. If it had arisen from glowing Hydrogen, it would likely have a frequency of one of the Balmer series of Hydrogen spectrum lines. NOT any of the other Balmer lines! So, a single Compton Effect encounter might shift one of the lines of the Hydrogen spectrum by some red-shift, but the rest of the lines would not then be shifted. THAT would not explain it.
It would be more likely to have to conclude that there were MANY Compton Effect like encounters along the way, so many that statistical analysis would apply. That seems to be the only way where all of the various spectral lines would thus be shifted by similar amounts. There are assorted theoretical problems in such multitudes of small shifts, particularly the alteration regarding the direction of the propagation of the photons. They would probably then no longer seem to have come from a single source.
A specific example is an apparent consequence of relativity's time dilation. It is commonly accepted that a rapidly receding (or approaching) astronaut in a spacecraft would age more slowly than his twin brother left back on Earth, because of the effect of time dilation. If we had a strong enough telescope to see him, he would appear to be moving in slow motion! Now say that he had a container of glowing hydrogen in his spacecraft. The motion of those atoms of hydrogen would also seem to us to be moving more slowly, for the same time dilation reason. The result would be that the oscillation frequency of the hydrogen atoms would appear to be lower, which would appear to be a red shift to us.
This same effect should exist in any glowing star that is receding at
relativistic velocities. In some cases, the red shift caused by this
Time Dilation Effect is as much as 1/3 the size of the Relativistic
Doppler Effect. An implication is that "real" Doppler
shifts for very distant objects might only be 3/4 as great as previously
thought. That would indicate that such objects are actually much closer
than previously thought and they were receding as less velocity. These
are huge implications, which could reflect on the scale of the Universe
and many other things. I wrote a separate presentation on that subject,
which is at:
http://mb-soft.com/public/reltvty2.html
( http://mb-soft.com/public/index.html )
C Johnson, Physicist, Physics Degree from Univ of Chicago