Noncommutative Geometry Spectral Action as a framework for unification:
  Introduction and phenomenological/cosmological consequences
  I will summarize Noncommutative Geometry Spectral Action, an elegant
geometrical model valid at unification scale, which offers a purely
gravitational explanation of the Standard Model, the most successful
phenomenological model of particle physics. Noncommutative geometry states that
close to the Planck energy scale, space-time has a fine structure and proposes
that it is given as the product of a four-dimensional continuum compact
Riemaniann manifold by a tiny discrete finite noncommutative space. The
spectral action principle, a universal action functional on spectral triples
which depends only on the spectrum of the Dirac operator, applied to this
almost commutative product geometry, leads to the full Standard Model,
including neutrino mixing which has Majorana mass terms and a see-saw
mechanism, minimally coupled to gravity. It also makes various predictions at
unification scale. I will review some of the phenomenological and cosmological
consequences of this beautiful and purely geometrical approach to unification.
