Noncommutative Spectral Geometry: A Short Review

TL;DR

This review discusses noncommutative spectral geometry as a unified framework for gravity and particle physics, highlighting its successes, limitations, and implications for early universe cosmology.

Contribution

It provides a comprehensive overview of noncommutative spectral geometry, emphasizing its potential to unify fundamental interactions and its cosmological applications.

Findings

Phenomenologically successful but predicts a Higgs mass discrepancy.

Offers a high-energy framework relevant for early universe cosmology.

Highlights need for extending the simple model to match experimental data.

Abstract

We review the noncommutative spectral geometry, a gravitational model that combines noncommutative geometry with the spectral action principle, in an attempt to unify General Relativity and the Standard Model of electroweak and strong interactions. Despite the phenomenological successes of the model, the discrepancy between the predicted Higgs mass and the current experimental data indicate that one may have to go beyond the simple model considered at first. We review the current status of the phenomenological consequences and their implications. Since this model lives by construction at high energy scales, namely at the Grand Unified Theories scale, it provides a natural framework to investigate early universe cosmology. We briefly review some of its cosmological consequences.