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

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.

11 pages; Invited contribution for Mario Castagnino's Festschrift, to be published in IJMPD

References in corpus (12)

• The Spectral Action Principle
• Gravity and the standard model with neutrino mixing
• A Universal Action Formula
• A Lorentzian version of the non-commutative geometry of the standard model of particle physics
• Why the Standard Model
• Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model
• Cosmology and the Noncommutative approach to the Standard Model
• The Uncanny Precision of the Spectral Action
• Inflation in models with Conformally Coupled Scalar fields: An application to the Noncommutative Spectral Action
• Natural inflation mechanism in asymptotic noncommutative geometry
• Scale Invariance in the Spectral Action
• Asymptotic Conformal Invariance of SU(2) and Standard Models in Curved Space-time

Cited by in corpus (10)

• Probing Models of Extended Gravity using Gravity Probe B and LARES experiments
• Particle Physics from Almost Commutative Spacetimes
• Constraints on NonCommutative Spectral Action from Gravity Probe B and Torsion Balance Experiments
• Noncommutative spectral geometry, algebra doubling and the seeds of quantization
• Noncommutative spectral geometry, dissipation and the origin of quantization
• Noncommutative Spectral Geometry: A Short Review
• Precession shift in curvature based Extended Theories of Gravity and Quintessence fields
• Aspects of the Bosonic Spectral Action
• Post-Newtonian N-Body Dynamics in Extended Theories of Gravity
• Noncommutative spectral geometry and the deformed Hopf algebra structure of quantum field theory