Non-slow-roll dynamics in $\alpha-$attractors

TL;DR

This paper investigates non-slow-roll inflation within $ ext{alpha}$-attractor models, demonstrating their broader applicability and compatibility with observational data, and analyzing the influence of model parameters on inflationary dynamics.

Contribution

It introduces a non-slow-roll approach to $ ext{alpha}$-attractors, expanding the class of viable inflationary models and linking dynamics to the $ ext{alpha}$ parameter and supergravity geometry.

Findings

Predicts $n_s oughly 0.967$ and $r oughly 5.5 imes 10^{-4}$ for a specific model.

Shows $ ext{alpha}$-attractors can accommodate $r<0.1$ under non-slow-roll dynamics.

Connects inflaton dynamics to the $ ext{alpha}$ parameter and Kähler manifold curvature.

Abstract

In this paper we consider the $\alpha-$attractor model and study inflation under a non-slow-roll dynamics. More precisely, we follow the approach recently proposed by Gong and Sasaki \cite{Gong:2015ypa} by means of assuming $N=N\left(\phi\right)$. Within this framework we obtain a family of functions describing the local shape of the potential during inflation. We study a specific model and find an inflationary scenario predicting an attractor at $n_{s}\approx0.967$ and $r\approx5.5\times10^{-4}$. We further show that considering a non-slow-roll dynamics, the $\alpha-$attractor model can be broaden to a wider class of models that remain compatible with value of $r<0.1$. We further explore the model parameter space with respect to large and small field inflation and conclude that the inflaton dynamics is connected to the $ \alpha- $ parameter, which is also related to the K\"ahler manifold curvature in the supergravity (SUGRA) embedding of this model. We also comment on the stabilization of the inflaton's trajectory.