  In this paper, we analyze the early-time inflation in a scalar-tensor theory
of gravity where the scalar field is minimally coupled with the Gauss-Bonnet
four dimensional topological invariant. The theory belongs to a class of
Horndeski models where the field equations are at the second order like in
General Relativity. A viable inflationary scenario must correctly reproduce the
last Plank satellite data. By starting from some simple assumptions on the
field and on the coupling function between the field and the Gauss-Bonnet term,
we derive the spectral index and the tensor-to-scalar ratio of the model. Once
the model is viable, it is finally possible to fully reconstruct its
Lagrangian.
