  The standard electroweak theory of leptons and the conformal groups of
spacetime Weyl's transformations are at the core of a general relativistic,
conformally covariant scalar tensor theory aimed at the resolution of the most
intriguing enigma of modern Physics: the cosmological constant paradox
(hereafter: Lambda paradox. A Higgs mechanism within a spontaneous symmetry
breaking process offers formal connections, via an effective potential V(eff),
between some relevant properties of the elementary particles and the dark
energy content of the Universe. The nonintegrable application of the Weyl's
geometry leads to a Proca equation accounting for the dynamics of a
vector-meson proposed as an optimum candidate for Dark Matter. The average
vacuum-energy density in the Universe and the "cosmological constant" are
evaluated on the basis of the recent experimental data of the PLANCK Mission.
The resolution of the paradox is found for all exponential inflationary
potentials and is consistent with the experimental data. The result of the
theory: Lambda=6|V(eff)|shows that the paradox is determined by the algebraic
mismatch between two large counteracting functions of the scalar field
contributing to V(eff). The critical stability of the Universe is discussed.
