Aspects of the Bosonic Spectral Action

TL;DR

This paper explores noncommutative spectral geometry for unification, discussing algebra doubling, phenomenological and cosmological implications, and introducing a zeta function regularisation approach for the bosonic spectral action.

Contribution

It introduces a novel spectral action method using zeta function regularisation to improve upon traditional cutoff-based approaches.

Findings

Constraint on unification coupling constants.

Implications of algebra doubling for physics.

Potential roles of scalar fields in cosmology.

Abstract

A brief description of the elements of noncommutative spectral geometry as an approach to unification is presented. The physical implications of the doubling of the algebra are discussed. Some high energy phenomenological as well as various cosmological consequences are presented. A constraint in one of the three free parameters, namely the one related to the coupling constants at unification, is obtained, and the possible role of scalar fields is highlighted. A novel spectral action approach based upon zeta function regularisation, in order to address some of the issues of the traditional bosonic spectral action based on a cutoff function and a cutoff scale, is discussed.