On the de Sitter Tardyons and Tachyons

It is shown that on the de Sitter manifolds the tachyonic geodesics are restricted such that the classical tachyons cannot exist on this manifold at any time. On the contrary, the theory of the scalar quantum tachyons is free of any restriction. The tachyonic scalar and Dirac plane waves are deduced in this geometry, pointing out that these are well-defined, behaving as tempered distributions at any moment.