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This article proposes some cosmological reflections at the qualitative andconjectural level, suggested by the Fantappie & Arcidiacono projectiverelativity theory. The difference will firstly be discussed between two typesof singularity in this theory: geometric (de Sitter horizon) and physical (bigbang, big crunch). The reasons for the existence of geometric singularities aredeeply rooted in the principle of inertia and in the principle of relativity,while physical singularities are associated with the creation or destruction ofmatter. In this framework, quantum mechanics is introduced through a particularinterpretation of Bohm holomovement. Finally, a possible mechanism is discussedfor the genesis of the cosmological term. No form of inflation appears in thescenario described.

The Archaic Universe: Big Bang, Cosmological Term and the Quantum Origin of Time in Projective Cosmology