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I will summarize Noncommutative Geometry Spectral Action, an elegantgeometrical model valid at unification scale, which offers a purelygravitational explanation of the Standard Model, the most successfulphenomenological model of particle physics. Noncommutative geometry states thatclose to the Planck energy scale, space-time has a fine structure and proposesthat it is given as the product of a four-dimensional continuum compactRiemaniann manifold by a tiny discrete finite noncommutative space. Thespectral action principle, a universal action functional on spectral tripleswhich depends only on the spectrum of the Dirac operator, applied to thisalmost commutative product geometry, leads to the full Standard Model,including neutrino mixing which has Majorana mass terms and a see-sawmechanism, minimally coupled to gravity. It also makes various predictions atunification scale. I will review some of the phenomenological and cosmologicalconsequences of this beautiful and purely geometrical approach to unification.

Noncommutative Geometry Spectral Action as a framework for unification: Introduction and phenomenological/cosmological consequences