Cosmology within Noncommutative Spectral Geometry

TL;DR

This paper explores how noncommutative spectral geometry provides a unified geometric framework for the standard model of particle physics and early universe cosmology, linking high-energy physics and cosmological phenomena.

Contribution

It demonstrates how spectral action in noncommutative geometry explains the standard model and offers insights into early universe cosmology at high energies.

Findings

Spectral action reproduces standard model particle physics.

Constraints on gravitational sector from cosmological data.

Framework unifies gravity and gauge interactions at high energies.

Abstract

Close to the Planck energy scale, the quantum nature of space-time reveals itself and all forces, including gravity, should be unified so that all interactions correspond to just one underlying symmetry. In the absence of a full quantum gravity theory, one may follow an effective approach and consider space-time as the product of a four-dimensional continuum compact Riemanian manifold by a tiny discrete finite noncommutative space. Since all available data are of a spectral nature, one may argue that it is more appropriate to apply the spectral action principle in this almost commutative space. Following this procedure one obtains an elegant geometric explanation for the most successful particle physics model, namely the standard model (and supersymmetric extensions) of electroweak and strong interactions in all its details, as determined by experimental data. Moreover, since this gravitational theory lives by construction at very high energy scales, it offers a perfect framework to address some of the early universe cosmological questions still awaiting for an answer. After introducing some of the main mathematical elements of noncommutative spectral geometry, I will discuss various cosmological and phenomenological consequences of this theory, focusing in particular on constraints imposed on the gravitational sector of the theory.