Unity of Cosmological Inflation Attractors

Recently, several broad classes of inflationary models have been discovered whose cosmological predictions, in excellent agreement with Planck, are stable with respect to significant modifications of the inflaton potential. Some classes of models are based on a nonminimal coupling to gravity. These models, which we call xi 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 alpha attractors. The aim of this Letter is to elucidate the common denominator of these attractors: their robust predictions stem from a joint pole of order 2 in the kinetic term of the inflaton field in the Einstein frame formulation prior to switching to the canonical variables. Model-dependent differences only arise at subleading level in the kinetic term. As a final step towards the unification of the different attractors, we introduce a special class of xi attractors which is fully equivalent to a attractors with the identification alpha = 1 + (1/6 xi). While r is generically predicted to be of the order 1/N-2, there is no theoretical lower bound on r in this class of models.