Dears justinater22 and Jdizz,
I will try to give you some historical and technical explanations.
In 1916, Albert Einstein released his famous field equations of the gravitational field in the framework of the General Theory of Relativity (GTR). In 1917 he tried to apply them to the whole universe. In that framework, he did not originally understand how such equations work. In fact, he thought that the gravitational force should force the universe to collapse. As he was an endorser of the static universe, he inserted the cosmological constant in the field equations in order to stop the supposed collapse of the universe. In 1925, Alexander Friedmann showed that, by assuming the Cosmological Principle, i.e. the universe is homogeneous and isotropic elsewhere and for every observer put in every point (in other words, observers on Earth do not occupy an unusual or privileged location within the universe as a whole, judged as observers of the physical phenomena produced by uniform and universal laws of physics), a the cosmological solution of GTR implies that, differently from what Einstein thought, not only the universe do not collapse, but, instead, it expands. Clearly, in such a solution, it is not absolutely needed that Earth must be at the centre of the universe. In 1929, the Hubble observations of the cosmological redshift were interpreted like effective expansion of the universe and, in such an interpretation, they were found in perfect agreement with the Friedmann's solution of GRT. At that time, Einstein claimed that the introduction of the cosmological constant was the "biggest blunder" of his life. The model by Friedmann was further refined by Lemaitre, Robertson and Walker in the '30 and now is known like the Friedmann-Robertson-Walker model. Lemaitre showed that the model starts with a universe of null dimensions and introduced the term "primordial atom". The term "big-bang" was indeed introduced by Fred Hoyle in the '50, but originally it was a derogatory term, as Hoyle was an opposer of the expansion model.
In the latest '60, Hawking and Penrose showed that all the models which are not too much different from the Friedmann model must start from null dimensions (singularity theorems). The assumptions of the singularity theorems are considered reasonable by the majority of the Scientific Community. Hence, the expansion of the universe is a cosmological solution of GRT.
On the other hand, in 1998, Perlmutter, Schmidt, Riess and collaborators, through observations of distant supernovae, found new data which were interpreted like evidence that the expansion of the universe is accelerating.
Differently from an uniform expansion with constant velocity, the acceleration of the universe is NOT a cosmological solution of GTR. In order to achieve the acceleration of the universe, theorists usually re-insert the cosmological constant in Einstein field equations. The cosmological constant is interpreted like a "Dark Energy", i.e. an intrinsic curvature of the space-time which is not due to the mass-energy of the galaxies, indeed it is due to an unknown negative energy, the "vacuum energy".
The Iso-Relativity Theory by Santilli is a very good and interesting theory which generalizes Special Relativity (which is surely valid in vacuum), in the material mediums. It admits the existence of a redshift, called iso-redshift by Santilli, which is independent by the motion of both of the source and of the observer. Notice that Santilli was not the first theorist who proposed the presence of a redshift independent by the motion of both of the source and of the observer in cosmology, although he was the first theorist, in the end of '70, who proposed a physical explanation of the effect. Tired light is a class of hypothetical redshift mechanisms that was proposed as an alternative explanation for the redshift-distance relationship. These models have been proposed as alternatives to the metric expansion of space of which the Big Bang and the Steady State cosmologies are the most famous examples. The concept was first proposed in 1929 by Fritz Zwicky, who suggested that if photons lost energy over time through collisions with other particles in a regular way, the more distant objects would appear redder than more nearby ones. Following after Zwicky in 1935, Edwin Hubble and Richard Tolman compared recessional redshift with a non-recessional one, writing that they:
" ... both incline to the opinion, however, that if the red-shift is not due to recessional motion, its explanation will probably involve some quite new physical principles [... and] use of a static Einstein model of the universe, combined with the assumption that the photons emitted by a nebula lose energy on their journey to the observer by some unknown effect, which is linear with distance, and which leads to a decrease in frequency, without appreciable transverse deflection."
I think that Santilli's iso-redshift is an intriguing explanation of Zwicky's idea. In all honesty, I do not know if Santilli iso-redshift, i.e. the presence of a redshift independent by the motion of both of the source and of the observer, could really demonstrate the lack of universe's expansion. I think that it should deserve a better attention by the Scientific Community as it could have, in any case, very important implications in cosmology. For example, the age of the universe could be different, the Dark Energy could be not needed, etc.
On the other and, in my opinion, claiming that the Concordance Model, i.e. the Big-Bang Model plus Dark Energy which theoretically arises from GTR plus the cosmological constant, is a dogma is wrong. It is merely a model constructed to explain the cosmological observations which is founded on various assumptions, the correctness of GTR, the validity of the singularity theorem, the presence of the cosmological constant and the absence of a redshift independent by the motion of both of the source and of the observer. I am all in favour of being open minded about alternatives, but they must be properly formulated and plausible scientific proposals. This is the reason because I think that it could be a good thing to carefully compare all the data by Santilli's experiment, according to which the redness of the sun itself at sunset experiences a redshift without any relative motion, with the cosmological data. Maybe we could obtain new insights on cosmology.
