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

TL;DR

This paper reviews the Noncommutative Geometry Spectral Action framework, which geometrically unifies the Standard Model with gravity at high energies, predicting particle physics phenomena and cosmological implications.

Contribution

It introduces a geometrical model based on noncommutative geometry that unifies the Standard Model with gravity and includes neutrino masses and cosmological effects.

Findings

Predicts neutrino mixing and Majorana masses

Provides a geometric explanation for the Standard Model

Suggests phenomenological and cosmological consequences at unification scale

Abstract

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.