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

TL;DR

This paper conducts a Bayesian analysis of generalized $ ext{alpha}$-attractor inflationary models, exploring parameter spaces and identifying the model with $p=4$ as most favored by CMB data, with consistent tensor-to-scalar ratio predictions.

Contribution

It introduces a Bayesian framework for analyzing generalized $ ext{alpha}$-attractor models with different powers $p$, and evaluates their statistical support using CMB data.

Findings

The $p=4$ model is statistically preferred by CMB data.

All studied models favor a tensor-to-scalar ratio of approximately 0.0025.

Constraints on the parameter $ ext{alpha}$ are derived from the data.

Abstract

We perform a Bayesian study of a generalization of the basic $\alpha$-attractor T model given by the potential $V(\phi)=V_0\left[1-\text{sech}^{p}\left(\phi/\sqrt{6\alpha}M_{pl}\right)\right]$ where $\phi$ 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 $r\simeq 0.0025$.