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

Abstract

Cosmological $α$-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 inflaton potential. In this work we derive improved analytical predictions for the large-scale observables, whose dependence on the duration of reheating and the parameter $α$ 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 $α$. 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 $α$ parameter, we demonstrate that including the $α$-dependence of the scalar spectral tilt yields novel constraints on $α$. In particular, for small $α$, the scalar spectral tilt scales with $\log_{10}α$, regardless of the specific potential shape. For decreasing $α$, this eventually puts the models in tension with CMB measurements, bounding the magnitude of $α$ 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 $α$ for $α$-attractor T-models, $\log_{10}α = -4.2^{+5.4}_{-8.6}$ at $95\%$ C.L. .