Polynomial inflation models after BICEP2

Large field inflation models are favored by the recent BICEP2 that has detected gravitational wave modes generated during inflation. We study general large field inflation models for which the potential contains (constant) quadratic and quartic terms of inflaton field. We show, in this framework, those inflation models can generate the fluctuation with the tensor-to-scalar ratio of $0.2$ as well as the scalar spectral index of $0.96$: those are very close to the center value of the tensor-to-scalar ratio reported by BICEP2 as well as Planck. Finally, we briefly discuss the particle physics model building of inflation.