Singular $\alpha$-attractors

TL;DR

This paper introduces a new class of $oldsymbol{ ext{S-model}}$ potentials in $oldsymbol{ ext{$oldsymbol{ ext{α}}$-attractors}}$ that can address initial conditions and fit recent cosmological data by allowing various plateau and growth behaviors.

Contribution

It generalizes $ ext{$ ext{α}$-attractor}$ models to include singular potentials at the boundary, broadening the scope of inflationary scenarios and their compatibility with observations.

Findings

S-models can solve initial conditions problem.

They match a broad range of $n_s$ values with recent data.

Potential behaviors include polynomial and exponential growth.

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.