Novel CMB constraints on the $\hat{I}\pm$ parameter in alpha-attractor models

Abstract

Cosmological $\hat{I}\pm$-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 $\hat{I}\pm$ 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 $\hat{I}\pm$. 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 $\hat{I}\pm$ parameter, we demonstrate that including the $\hat{I}\pm$-dependence of the scalar spectral tilt yields novel constraints on $\hat{I}\pm$. In particular, for small $\hat{I}\pm$, the scalar spectral tilt scales with ${\log }_{10}\hat{I}\pm$, regardless of the specific potential shape. For decreasing $\hat{I}\pm$, this eventually puts the models in tension with CMB measurements, bounding the magnitude of $\hat{I}\pm$ 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 $\hat{I}\pm$ for $\hat{I}\pm$-attractor T-models, ${\log }_{10}\hat{I}\pm =-4.2_{-8.6}^{+5.4}$ at $95\%$ C.L. .

version accepted for publication in JCAP