Singular <i>α</i> -attractors

Abstract Inflationary α -attractor models naturally appear in supergravity with hyperbolic geometry. The simplest versions of α -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 φ . In a closely related class of polynomial α -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 α-attractors and may account for a very broad range of possible values of n s matching the recent ACT, SPT, and DESI data.