Non-minimally coupled Higgs inflation with Starobinsky gravity

We investigate the inflation model scenario generated by the Higgs field, where the field is non-minimally coupled to Starobinsky gravity. The slow-roll approximation is used to calculate the explicit form of two inflation observables: the tensor-to-scalar ratio (r) and the spectral index (ns). This model's tensor-to-scalar ratio (r) and spectral index (ns) values are calculated using three χ value limits: eχ ≫ 1, eχ >> 1, and eχ << 1. The observable value is compared with the Planck 2018 observation data. Only the eχ >> 1 limit, with values of (ns,r)N=50=(0.9605,0.0042) and (ns,r)N=60=(0.9671,0.0030), is suitable for the Planck Constraint 2018, while the other limits fall outside the 1σ range. The results are also consistent with the COBE normalization and Lyth Bound constraints.