Bayesian analysis for a class of α-attractor inflationary models

Abstract

We perform a Bayesian study of a generalization of the basic α-attractor T model given by the potential V(ϕ) = V 0[1-sech p (ϕ/√(6α)M pl)] where ϕ is the inflaton field and the parameter α corresponds to the inverse curvature of the scalar manifold in the conformal or superconformal realizations of the attractor models. Such generalization is characterized by the power p which includes the basic or base model for p = 2. Once the priors for the parameters of the α-attractor potential are set by numerical exploration, we perform the corresponding statistical analysis for the cases p = 1, 2, 3, 4, and derive posteriors. Considering the original α-attractor potential as the base model, we calculate the evidence for our generalization, and conclude that the p = 4 model is preferred by the CMB data. We also present constraints for the parameter α. Interestingly, all the cases studied prefer a specific value for the tensor-to-scalar ratio given by r ≃ 0.0025.