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.

Novel CMB constraints on the α parameter in alpha-attractor models

“…(3.13). Similar to our results, see figure 4, they also find n s is correlated with α. Interestingly, according to the analysis of [66], these α-attractors seem to prefer the specific value r ≃ 0.0025. We suspect that this result strongly depends on the prior chosen for α, which in [66] is bounded from below due to numerical precision issues and adopts a uniform linear prior.…”

“…Similar to our results, see figure 4, they also find n s is correlated with α. Interestingly, according to the analysis of [66], these α-attractors seem to prefer the specific value r ≃ 0.0025. We suspect that this result strongly depends on the prior chosen for α, which in [66] is bounded from below due to numerical precision issues and adopts a uniform linear prior. As demonstrated in this work, the constraints on α change depending on the choice of prior, and therefore allowed r values will change accordingly (since r is strongly correlated with α, see figure 4).…”

“…In [66] the authors perform a Bayesian analysis of a generalisation of α-attractor T-models. Their posterior analysis shows a correlation between the parameter α and ∆N CMB , which we analytically justify, see eq.…”

“…As demonstrated in this work, the constraints on α change depending on the choice of prior, and therefore allowed r values will change accordingly (since r is strongly correlated with α, see figure 4). It would be interesting to explicitly assess the impact of different prior choices in the context of the analysis of [66].…”