Polynomial $\alpha$-attractors

TL;DR

This paper introduces polynomial $oldsymbol{ extit{ extalpha}}$-attractors, a new class of inflationary models with polynomial approach to the plateau, expanding the landscape of supergravity-based inflation models consistent with current observational data.

Contribution

The paper proposes polynomial $oldsymbol{ extit{ extalpha}}$-attractors, a novel class of inflation models with non-singular potentials whose derivatives are singular at the boundary, complementing exponential $oldsymbol{ extit{ extalpha}}$-attractors.

Findings

Polynomial $ extit{ extalpha}$-attractors fit Planck/BICEP/Keck data.

They feature a plateau potential approached polynomially.

Models cover the full observationally favored parameter space.

Abstract

Inflationary $\alpha$-attractor models can be naturally implemented in supergravity with hyperbolic geometry. They have stable predictions for observables, such as $n_s=1-{2/ N_e} $, assuming that the potential in terms of the original geometric variables, as well as its derivatives, are not singular at the boundary of the hyperbolic disk, or half-plane. In these models, the potential in the canonically normalized inflaton field $\varphi$ has a plateau, which is approached exponentially fast at large $\varphi$. We call them exponential $\alpha$-attractors. We present a closely related class of models, where the potential is not singular, but its derivative is singular at the boundary. The resulting inflaton potential is also a plateau potential, but it approaches the plateau polynomially. We call them polynomial $\alpha$-attractors. Predictions of these two families of attractors completely cover the sweet spot of the Planck/BICEP/Keck data. The exponential ones are on the left, the polynomial are on the right.