Aspects of the Bosonic Spectral Action: Successes and Challenges

TL;DR

This paper discusses the spectral action in noncommutative geometry, highlighting its successes, challenges, and a new zeta function regularisation approach, with implications for the Standard Model and cosmology.

Contribution

It introduces a novel spectral action proposal based on zeta function regularisation and analyzes its implications for physics and cosmology.

Findings

Higher derivative gravitational theory from noncommutative geometry

Cosmological stability of the gravitational sector

Introduction of zeta function regularisation in spectral action

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.