Reconstructing the local potential of inflation with BICEP2 data

We locally reconstruct the inflationary potential by using the current constraints on r and n_s from BICEP2 data. Assuming small and negligible α_s, the inflationary potential is approximately linear in Δφ∼ M_pl range but becomes non-linear in Δφ∼ 10 M_pl range. However if we vary the value of α_s within the range given by constraints from Planck measurement, the local reconstruction is only valid in the range of Δφ∼ 0.4 M_pl, which challenges the inflationary background from the point of view of effective field theory. We show that, within the range of Δ φ ∼ 0.4 M_pl, the inflation potential can be precisely reconstructed. With the current reconstruction, we show that V(φ) ∼ φ² and φ³ are consistent, while φ model is ruled out by 95% confidence level of the reconstructed range of potential. This sets up a strong limit of large-field inflation models.