# Reconstruction of extended inflationary potentials for attractors

## TL;DR

This paper presents a method to reconstruct extended inflationary potentials for attractors, demonstrating their consistency with observations and highlighting challenges in model discrimination based solely on $n_s$ and $r$.

## Contribution

It introduces a reconstruction procedure for extended inflationary potentials within attractor models, including the derivation of a strong coupling condition and analysis of observational consistency.

## Key findings

- Reconstructed potentials are consistent with observational constraints.
- Extended inflationary models share the same attractor behavior.
- The existence of attractors complicates model discrimination using $n_s$ and $r$.

## Abstract

We give the procedure to reconstruct the extended inflationary potentials for attractors and use the $\alpha$ attractor and the constant-roll model as examples to show how to reconstruct the class of extended inflationary potentials in the strong coupling limit. We also derive the strong coupling condition which the coupling constant $\xi$ satisfies. The class of extended inflationary potentials has the same attractor, and the reconstructed extended inflationary potentials are consistent with the observational constraints. The existence of the attractors from extended inflationary models further challenges the model discrimination just by the observables $n_s$ and $r$.