Higgs inflation with non-minimal derivative coupling to gravity

We consider an extension of Higgs inflation in which the Higgs field is non-minimally coupled to gravity through its kinetic term. We analyzed power-law coupling functions with positive or negative integer power and found that the Higgs boson can drive a successful inflation only for the cases $n=2,1,0,-1$. Theoretical predictions for both tensor to scalar ratio $r$ and scalar spectral index $n_s$ are within the 2018 $\mathit{\text{Planck}}$ $95\mathrm{\%}$ CL. The behavior of the self coupling $\lambda$ with respect to the scalar field at the horizon crossing was obtained, and It was found that it can take values in the interval $\lambda \sim ({10}^{-7},0.3)$.