The Unity of Cosmological Attractors

TL;DR

The paper investigates why a broad class of inflationary models—α-attractors, ξ-attractors, conformal, universal, and induced inflation—yield robust, nearly model-independent predictions. It identifies a unifying mechanism: a leading pole of order two in the inflaton's kinetic term in the Einstein frame, whose order fixes n_s and whose residue fixes r. By recasting ξ-attractors as α-attractors with α = 1 + 1/(6ξ) and introducing Special Attractors, the authors unify disparate attractor families and show that subleading corrections are largely irrelevant at large N. This framework clarifies the connections between Jordan and Einstein-frame formulations and broadens the landscape of viable inflationary models with tunable r without constraining a lower bound on its value.

Abstract

Recently, several broad classes of inflationary models have been discovered whose cosmological predictions are stable with respect to significant modifications of the inflaton potential. Some classes of models are based on a non-minimal coupling to gravity. These models, which we will call $ξ$-attractors, describe universal cosmological attractors (including Higgs inflation) and induced inflation models. Another class describes conformal attractors (including Starobinsky inflation and T-models) and their generalization to $α$-attractors. The aim of this paper is to elucidate the common denominator of these models: their attractor properties stem from a pole of order two in the kinetic term of the inflaton field in the Einstein frame formulation, prior to switching to the canonical variables. We point out that $α$- and universal attractors differ in the subleading corrections to the kinetic term. As a final step towards unification of $ξ$ and $α$ attractors, we introduce a special class of $ξ$-attractors which is fully equivalent to $α$-attractors with the identification $α= 1+{1\over 6ξ}$. There is no theoretical lower bound on $r$ in this class of models.

Figures (1)

• Figure 1: Unification of cosmological attractors. The new class of $\xi$-attractors, which we called special attractors, defined by (\ref{['lagEa']}), are fully equivalent to $\alpha$-attractors with $\alpha = 1+{1\over 6\xi}$.