Endlessly flat scalar potentials and $\alpha$-attractors

Abstract

We consider a minimally-coupled inflationary theory with a general scalar potential $V(f(\phi ))=V(\xi {\sum }_{k=1}^n{\lambda }_k{\phi }^k)$ 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.

8 pages, 2 figures

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