Reconstructing the Local Potential of Inflation with BICEP2 data

Abstract

We locally reconstruct the inflationary potential by using the current constraints on $r$ and $n_{\rm s}$ from BICEP2 data. Assuming small and negligible $α_{\rm s}$, the inflationary potential is approximately linear in $Δϕ\sim M_{\rm pl}$ range but becomes non-linear in $Δϕ\sim 10 M_{\rm pl}$ range. However if we vary the value of $α_{\rm s}$ within the range given by constraints from {\it Planck} measurement, the local reconstruction is only valid in the range of $Δϕ\sim 0.4 M_{\rm pl}$, which challenges the inflationary background from the point of view of effective field theory. We show that, within the range of $Δϕ\sim 0.4 M_{\rm pl}$, the inflation potential can be precisely reconstructed. With the current reconstruction, we show that $V(ϕ) \sim ϕ^{2}$ and $ϕ^{3}$ 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.