In this paper, we present systematic studies on the insufficiencies of special relativity within physical media, such as water, atmospheres and the interior of astrophysical bodies. We outline the rather large body of research on the deformations of special relativity applicable within physical media, known under the name of isotopies. We then present, apparently for the first time, experimental verifications of the hypothesis formulated by the author in 1991, and today known as isoredshift, according to which light propagating within a physical medium experiences a shift of its frequency toward the red without any relative motion between the source, the medium and the observer, the shift originating from expected loss of energy to the medium due to interactions. We then confirm the isoredshift in the colors of our atmosphere as well as in the large difference in cosmological redshift between certain quasars and their associated galaxies; we indicate the consequential conceivable absence of universe expansion, big bang, dark matter, and dark energy; and propose systematic tests for the resolution of cosmological models via experiments on Earth along the teaching of Galileo Galilei.

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