The formalism of Fantappié-Arcidiacono Projective General Relativity –also known as De Sitter Relativity- hasrecently been revised in order to make possible cosmological models with expansion, similarly to ordinary Friedmanncosmology formulated within the context of General Relativity. In this article, several consequences of interest in the currentcosmological debate are examined and discussed in a semiquantitative manner. Specifically: re-examination of theSupernova Project results using this new formalism, with a new estimate of the cosmological parameters; the ordinarymatter to dark matter densities ratio; the existence of a new fundamental constant having the dimensions of an accelerationand its relation with dark matter.
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