  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.
