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

Cosmological alpha-attractors are a compelling class of inflationary models. They lead to universal predictions for large-scale observables, broadly independent from the functional form of the inflation potential. In this work we derive improved analytical predictions for the large-scale observables, whose dependence on the duration of reheating and the parameter alpha is made explicit. We compare these with Planck and BICEP/Keck 2018 data in the framework of a Bayesian study, employing uniform logarithmic and linear priors for alpha. Our improved universal predictions allow direct constraints on the duration of reheating. Furthermore, while it is well-known that CMB constraints on the tensor-to-scalar ratio can be used to place an upper bound on the alpha parameter, we demonstrate that including the alpha-dependence of the scalar spectral tilt yields novel constraints on alpha. In particular, for small alpha, the scalar spectral tilt scales with log₁₀ alpha, regardless of the specific potential shape. For decreasing alpha, this eventually puts the models in tension with CMB measurements, bounding the magnitude of alpha from below. Therefore, in addition to the upper bound from the tensor-to-scalar ratio, we derive the first lower bound on the magnitude of alpha for alpha-attractor T-models, log₁₀ alpha = -4.2 (+5.4/-8.6) at 95% C.L. .