Bayesian analysis for a class of $\alpha$-attractor inflationary models

Abstract

We perform a Bayesian study of a generalization of the basic $\alpha$-attractor T model given by the potential $V(\varphi )=V_0\left[1-{\text{sech}}^p\left(\varphi /\sqrt{6\alpha }{M}_{pl}\right)\right]$ where $\varphi$ is the inflaton field and the parameter $\alpha$ 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 $\alpha$-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 $\alpha$-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 $\alpha$. Interestingly, all the cases studied prefer a specific value for the tensor-to-scalar ratio given by $r\simeq 0.0025$.

17 pages, 8 figures, 4 tables. Minor amendments to match the version published in JCAP

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Cited by in corpus (1)

• Development of generic no-scale inflation