Aspects of the Bosonic Spectral Action: Successes and Challenges

Abstract

A short introduction on elements of noncommutative geometry, which offers a purely geometric interpretation of the Standard Model and implies a higher derivative gravitational theory, is presented. Physical consequences of almost commutative manifolds are briefly discussed and cosmological consequences of the gravitational sector, which is shown not to be plagued by linear instability, are highlighted. Successes and challenges are discussed. A novel spectral action proposal based on zeta function regularisation is briefly presented.

10 pages. Invited talk to appear in the Proceedings of the Corfu Summer Institute 2015 "School and Workshops on Elementary Particle Physics and Gravity", 1-27 September 2015, Corfu, Greece

References in corpus (8)

• Resilience of the Spectral Standard Model
• Constraining the Noncommutative Spectral Action via Astrophysical Observations
• Inflation in models with Conformally Coupled Scalar fields: An application to the Noncommutative Spectral Action
• Grand Unification in the Spectral Pati-Salam Model
• Gravitational Waves in the Spectral Action of Noncommutative Geometry
• Spectral dimensions from the spectral action
• Linear stability of noncommutative spectral geometry
• Aspects of the Bosonic Spectral Action