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Higgs Inflation in f(Φ,R) Theory

We generalize the scalar-curvature coupling model ${ξΦ^2 R}$ of Higgs inflation to $ {ξΦ^a R^b} $ to study inflation. We compute the amplitude and spectral index of curvature perturbations generated during inflation and fix the parameters of the model by comparing these with the Planck$+$WP data. We find that if the scalar self coupling $λ$ is in the range $(10^{-5}-0.1)$, parameter $a$ in the range $(2.3 -3.6)$ and $b$ in the range $(0.77-0.22)$ at the Planck scale, one can have a viable inflation model even for $ξ\simeq 1$. The tensor to scalar ratio $r$ in this model is small and our model with scalar-curvature couplings is not ruled out by observational limits on $r$ unlike the pure $\fracλ{4} Φ^4$ theory. By requiring the curvature coupling parameter to be of order unity, we have evaded the problem of unitarity violation in scalar-graviton scatterings which plague the $ξΦ^2 R$ Higgs inflation models. We conclude that the Higgs field may still be a good candidate for being the inflaton in the early universe if one considers higher dimensional curvature coupling.