The hybrid Higgs inflation model is a hybrid type of the so-called Higgs inflation model with the conventional nonminimal ζ coupling to a scalar curvature R and the new Higgs inflation model with the derivative coupling to the Einstein curvature tensor Gμν. This model can explain all possible values of the tensor-to-scalar ratio r allowed by the present cosmic microwave background constraints with an appropriate choice of coupling parameters. However, the derivative coupling may cause a gradient instability during the oscillation phase after inflation just as in the new Higgs inflation model. Analyzing the behavior of perturbations during the oscillation phase in the hybrid Higgs inflation model, we show that the unstable scalar modes found in the new Higgs inflation model are stabilized by the nonminimal ζ coupling for some range of the coupling parameters.
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