Higgs Inflation with linear and quadratic curvature corrections

We consider a single scalar field inflation model with Higgs potential and curvature corrections given by non-minimal derivative coupling to gravity and coupling to the Gauss-Bonnet invariant. Exact analytical expressions, within the slow-roll approximation, are obtained for the main physical quantities. These corrections lead to successful inflation driven by the $\phi^4$-potential with the main inflationary observables in the regions restricted by the latest Planck data. It is shown that these curvature corrections can make the $\phi^4$ potential not only compatible with the current CMB observations, but also consistent with the Standard Model Higgs phenomenology, achieving the possibility that the Higgs boson acts as the primordial inflaton.