Higgs Inflation with a Gauss-Bonnet term

TL;DR

This paper explores Higgs inflation incorporating a Gauss-Bonnet term, revealing new interactions and demonstrating consistency with observational data and gravitational wave constraints across a broad parameter range.

Contribution

It introduces a simplified model with coupled functions, analyzes the resulting interactions in the Einstein frame, and shows observational viability and stability of gravitational waves.

Findings

Model aligns with observational data for a wide parameter range.

Emergence of non-minimal kinetic and derivative self-interactions.

Gravitational wave speed remains consistent with recent constraints.

Abstract

Higgs inflation with a Gauss-Bonnet term is studied in the Einstein frame. Our model features two coupling functions, $\Omega^2(\phi)$ and $\omega(\phi)$, coupled to the Ricci scalar and Gauss-Bonnet combinations. We found a special relation $\Omega^2 \propto \omega$ sets the system a lot more simplified; therefore, we take it for granted in our analytical studies. As a result of a Weyl transformation to the Einstein frame, we notice the emergence of new interactions: a non-minimal kinetic coupling between the scalar field and gravity and a derivative self-interaction of the scalar field. In the Einstein frame, we investigate the cosmological implications of these interactions by deriving the background equation of motion and observable quantities. Our numerical result on $n_S$ vs. $r$ suggests our model is consistent with the observational data for a wide range of the model parameter, $-1.4\times 10^4\lesssim \alpha \equiv \frac{\omega}{\Omega^2} \lesssim 8\times 10^3$, where both the positive and negative values of $\alpha$ are allowed. As the Gauss-Bonnet contributions decay away with time after inflation, the propagation speed of gravitational waves turned out to be consistent with the recent constraints on the propagation speed of gravitational waves (GWs) without inducing ghost instability.