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