Fantappi\'e-Arcidiacono theory of relativity versus recent cosmological evidences : a preliminary comparison

Notwithstanding the Fantappie-Arcidiacono theory of relativity was introduced more than half a century ago, its observational confirmations in cosmology (the only research field where its predictions differ from those of the Einsteinian relativity) are still missing. In line of principle, this theory may be proposed as a valid alternative to the current views assuming the dominance of dark matter and inflationary scenarios. In this work, the relativistic transformation of the Poynting vector associated with the reception of electromagnetic waves emitted by astronomical obiects is derived in the context of the special version of the theory. On the basis of this result, and some heuristic assumptions, two recent collections of observational data are analyzed.