Singular $\alpha$-attractors

Renata Kallosh; Andrei Linde

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arXiv · 2512.02969

Singular $\alpha$-attractors

Renata Kallosh·Andrei Linde

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Abstract

$\alpha$-attractor models naturally appear in supergravity with hyperbolic geometry. The simplest versions of $\alpha$-attractors, T- and E-models, originate from theories with non-singular potentials. In canonical variables, these potentials have a plateau that is approached exponentially fast at large values of the inflaton field $\varphi$. In a closely related class of polynomial $\alpha$-attractors, or P-models, the potential is not singular, but its derivative is singular at the boundary. The resulting inflaton potential also has a plateau, but it is approached polynomially. In this paper, we will consider a more general class of potentials, which can be singular at the boundary of the moduli space, S-models. These potentials may have a short plateau, after which the potential may grow polynomially or exponentially at large values of the inflaton field. We will show that this class of models may provide a simple solution to the initial conditions problem for $\alpha$-attractors and may account for a very broad range of possible values of $n_{s}$ matching the recent ACT, SPT, and DESI data.

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Renata Kallosh, Andrei Linde. 2025-12-02. Singular $\alpha$-attractors. https://arxiv.org/abs/2512.02969

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