Two-field inflation with non-minimal coupling

Motivated by the recent `Higgs-inflation' scenario based on a single inflaton field, we consider more generic two-field inflation with non-minimal coupling term. The generic analytic expressions are derived for cosmological observables with the product-separable as well as additive-separable potentials when the non-minimal coupling term is dominated by one of the two fields. A hybrid model of the inflaton potential $V=\mu^2 \phi^2 \left[1+\cos(\chi/\sigma)\right]$ with a non-minimal coupling $K=\alpha \phi$, which guarantees the flatness, is closely examined as a concrete example. Compared to the minimal model with $K=0$, the non-minimal model is shown to provide better fit to the recent cosmological observation by WMAP9 and Planck2013 with the relatively lower field values during the inflationary epoch. Most interestingly, a small value of tensor-to-scalar ratio requires a large non-minimal coupling in our scenario. The model produces non-observably small non-Gaussianity in most of parameter space while a large non-Gaussianity($\sim {\mathcal O}(10)$) is obtainable only when the inflation takes place in a limited field space along the top of the potential.