Cosmological Attractor Models and Higher Curvature Supergravity

TL;DR

This work establishes a detailed classical duality between two-derivative supergravity with two chiral multiplets and higher-derivative $R^2$-type supergravities across a broad class of cosmological α-attractor models. For α=1, a tractable duality relates the standard matter content to a curvature-dominated theory, with pure higher-derivative gravity arising only in the special Cecotti limit F(T)=aT+b; for generic superpotentials, at least one scalar remains in the dual. When stabilization terms are included, the duality persists under certain T-independent constructions, yielding explicit mass formulas and conditions (e.g., $g>1/6$) that ensure tachyon-free evolution. For general α-attractors, the dual theories either retain the same number of scalars or reduce only in special cases, with the holomorphic sectional curvature in the inflaton direction fixed to $-\frac{2}{3\alpha}$, tying geometric data to inflationary observables. Overall, the paper delineates how upcoming measurements of $n_s$ and $r$ could reveal whether the inflaton is a fundamental multiplet or a curvature excitation within higher-derivative supergravity frameworks, thereby connecting cosmology, supersymmetry, and geometric properties of the moduli space.

Abstract

We study cosmological $α$-attractors in superconformal/supergravity models, where $α$ is related to the geometry of the moduli space. For $α=1$ attractors \cite{Kallosh:2013hoa} we present a generalization of the previously known manifestly superconformal higher curvature supergravity model \cite{Cecotti:1987sa}. The relevant standard 2-derivative supergravity with a minimum of two chiral multiplets is shown to be dual to a 4-derivative higher curvature supergravity, where in general one of the chiral superfields is traded for a curvature superfield. There is a degenerate case when both matter superfields become non-dynamical and there is only a chiral curvature superfield, pure higher derivative supergravity. Generic $α$-models \cite{Kallosh:2013yoa} interpolate between the attractor point at $α=0$ and generic chaotic inflation models at large $α$, in the limit when the inflaton moduli space becomes flat. They have higher derivative duals with the same number of matter fields as the original theory or less, but at least one matter multiplet remains. In the context of these models, the detection of primordial gravity waves will provide information on the curvature of the inflaton submanifold of the Kahler manifold, and we will learn if the inflaton is a fundamental matter multiplet, or can be replaced by a higher derivative curvature excitation.