Endlessly flat scalar potentials and $\alpha$-attractors

TL;DR

This paper explores how infinitely flat scalar potentials relate to stationary points of infinite order in inflationary models, connecting these concepts to the framework of $oldsymbol{ extalpha}$-attractors.

Contribution

It introduces a method to associate asymptotically flat potentials with stationary points of infinite order, advancing the understanding of inflationary scalar potentials and their relation to $oldsymbol{ extalpha}$-attractors.

Findings

Asymptotically flat potentials linked to infinite order stationary points.

Established connection between flat potentials and $oldsymbol{ extalpha}$-attractors.

Provided a theoretical framework for analyzing scalar potentials in inflation.

Abstract

We consider a minimally-coupled inflationary theory with a general scalar potential $V(f(\varphi))= V(\xi\sum_{k=1}^{n}\lambda_k \varphi^k)$ containing a stationary point of maximal order $m$. We show that asymptotically flat potentials can be associated to stationary points of infinite order and discuss the relation of our approach to the theory of $\alpha$-attractors.