The Reconstruction of Non-Minimal Derivative Coupling Inflationary Potentials

Abstract

We derive the reconstruction formulae for the inflation model with the non-minimal derivative coupling term. If reconstructing the potential from the tensor-to-scalar ratio, we could obtain the potential without using the high friction limit. As an example, we reconstruct the potential from the parametrization $r=8\alpha /(N+\beta {)}^{\gamma }$, which is a general form of the $\alpha$-attractor. The reconstructed potential has the same asymptotic behavior as the T- and E-model if we choose $\gamma =2$ and $\alpha \ll 1$. We also discuss the constraints from the reheating phase preceding the radiation domination by assuming the parameter $w_{re}$ of state equation during reheating is a constant. The scale of big-bang nucleosynthesis could put a up limit on $n_s$ if $w_{re}=2/3$ and a low limit on $n_s$ if $w_{re}=1/6$.

arXiv comment12 pages, 3 figures

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