  In the last years the traditional scenario of Big Bang has been deeply
modified by the study of the quantum features of the Universe evolution,
proposing again the problem of using local physical laws on cosmic scale, with
particular regard to the cosmological constant role. The group extention method
shows that the De Sitter group univocally generalizes the Poincare group,
formally justifies the cosmological constant use and suggests a new
interpretation for Hartle-Hawking boundary conditions in Quantum Cosmology.
