Reconstructing the Local Potential of Inflation with BICEP2 data

Abstract

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

arXiv comment11 pages, 10 figures

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• Compensation for large tensor modes with iso-curvature perturbations in CMB anisotropies
• Reconstruction of $\alpha$-attractor supergravity models of inflation
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