Universality of multi-field $\alpha$-attractors

Abstract

We study a particular version of the theory of cosmological $\alpha$-attractors with $\alpha =1/3$, in which both the dilaton (inflaton) field and the axion field are light during inflation. The kinetic terms in this theory originate from maximal $\mathcal{N}=4$ superconformal symmetry and from maximal $\mathcal{N}=8$ supergravity. We show that because of the underlying hyperbolic geometry of the moduli space in this theory, it exhibits double attractor behavior: their cosmological predictions are stable not only with respect to significant modifications of the dilaton potential, but also with respect to significant modifications of the axion potential: $n_s\simeq 1-\frac{2}{N}$, $r\simeq \frac{4}{N^2}$. We also show that the universality of predictions extends to other values of $\alpha \lesssim \mathcal{O}(1)$ with general two-field potentials that may or may not have an embedding in supergravity. Our results support the idea that inflation involving multiple, not stabilized, light fields on a hyperbolic manifold may be compatible with current observational constraints for a broad class of potentials.

26 pages, 9 figures; v2: published version with references added and discussion extended

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