Inflationary Cosmology from Noncommutative Geometry

TL;DR

This paper explores how noncommutative geometry-based gauge theories can naturally lead to chaotic inflation in the early universe, with scalar fields influencing space-time structure without symmetry breaking.

Contribution

It investigates inflationary dynamics within a noncommutative geometry framework, highlighting the natural emergence of chaotic inflation from simple abelian models.

Findings

Chaotic inflation is naturally favored in the model.

No symmetry breaking occurs during inflation.

The final space-time separation decreases with more e-folds.

Abstract

In the framework of the Connes-Lott model based on noncommutative geometry, the basic features of a gauge theory in the presence of gravity are reviewed, in order to show the possible physical relevance of this scheme for inflationary cosmology. These models naturally contain at least two scalar fields, interacting with each other whenever more than one fermion generation is assumed. In this paper we propose to investigate the behaviour of these two fields (one of which represents the distance between the copies of a two-sheeted space-time) in the early stages of the universe evolution. In particular the simplest abelian model, which preserves the main characteristics of more complicate gauge theories, is considered and the corresponding inflationary dynamics is studied. We find that a chaotic inflation is naturally favoured, leading to a field configuration in which no symmetry breaking occurs and the final distance between the two sheets of space-time is smaller the greater the number of $e$-fold in each sheet.