Inflation in models with Conformally Coupled Scalar fields: An application to the Noncommutative Spectral Action

TL;DR

This paper investigates slow-roll inflation with conformally coupled scalar fields, focusing on Higgs inflation within the noncommutative spectral action, and examines the impact of additional scalar fields on inflationary predictions and their compatibility with observational data.

Contribution

It analyzes the viability of Higgs and additional scalar fields for inflation in noncommutative geometry, highlighting constraints from CMB data and particle physics.

Findings

Higgs potential can satisfy slow-roll conditions with two-loop running of self-coupling.

Predictions are incompatible with the measured top quark mass.

Additional conformally coupled scalar fields influence inflationary dynamics.

Abstract

Slow-roll inflation is studied in theories where the inflaton field is conformally coupled to the Ricci scalar. In particular, the case of Higgs field inflation in the context of the noncommutative spectral action is analyzed. It is shown that while the Higgs potential can lead to the slow-roll conditions being satisfied once the running of the self-coupling at two-loops is included, the constraints imposed from the CMB data make the predictions of such a scenario incompatible with the measured value of the top quark mass. We also analyze the role of an additional conformally coupled massless scalar field, which arises naturally in the context of noncommutative geometry, for inflationary scenarios.