Inflationary $\alpha$-Attractor Models with Singular Derivative of Potential

TL;DR

This paper explores a generalized class of inflationary $ ext{alpha}$-attractor models with singular derivatives in the potential, showing they can produce viable inflationary predictions and potential dark matter and gravitational wave signals.

Contribution

It introduces a systematic analysis of polynomial $ ext{alpha}$-attractor models with singular derivatives, expanding the understanding of their inflationary predictions and observational prospects.

Findings

Models predict larger $n_s$ and $r$ than standard $ ext{alpha}$-attractors.

Viable inflationary observables are achievable without a pole in the kinetic term.

Potential modifications can produce primordial black holes and detectable gravitational waves.

Abstract

A generalization of inflationary $\alpha$-attractor models (``polynomial $\alpha$-attractor'') was recently proposed by Kallosh and Linde, in which the potential involves logarithmic functions of the inflaton so that the derivative of the potential but not potential itself has a singularity. We find that the models can lead to viable inflationary observables even without the pole in the kinetic term. Also, the generalization with a pole order other than two does not significantly change the functional form of the potential. This allows a systematic analysis of the predictions of this class of models. Our models predict larger spectral index $n_s$ and tensor-to-scalar ratio $r$ than in the polynomial $\alpha$-attractor: typically, $n_s$ around 0.97--0.98 and $r$ observable by LiteBIRD. Taking advantage of the relatively large $n_s$, we discuss the modification of the potential to produce primordial black holes as the whole dark matter and gravitational waves induced by curvature perturbations detectable by LISA and BBO/DECIGO, while keeping $n_s$ in agreement with the Planck/BICEP/Keck data.