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We examine cosmological inflation in a broad family of scalar-tensor modelscharacterized by scalar-dependent non minimal kinetic couplings andGauss-Bonnet terms. Using a slow roll-approximation, we compute in detailtheoretical expectations of observables as spectral indexes, scalar-to-tensorratio, their running and their running of the running in terms of theparameters which characterize the scalar-tensor model. Hierarchies ofconsistency equations relating scalar and tensor pertubations and higher orderrunning parameters are presented and examined at the slow roll approximationfor the kind of models of interest in this work. From We find detailedexpressions for constraints among these parameters. For a specific model, weanalyse such quantities and make contact with latest Planck observational data .

Reconstructing slow-roll Scalar-Tensor Gauss-Bonnet single field inflation from running spectral data