The Reconstruction of Non-Minimal Derivative Coupling Inflationary Potentials

TL;DR

This paper develops a method to reconstruct inflationary potentials with non-minimal derivative coupling from observational data, avoiding the high friction limit, and explores constraints from the reheating phase.

Contribution

It introduces reconstruction formulae for non-minimal derivative coupling inflation models directly from the tensor-to-scalar ratio, expanding the tools for analyzing such models.

Findings

Reconstructed potential exhibits asymptotic behavior similar to T- and E-models.

Derived constraints on the spectral index from reheating parameters.

Provided a generalized form of the potential for $eta$-attractor models.

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 $\alpha\ll1$. 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 $w_{re}=1/6$.