$\alpha$-attractors from supersymmetry breaking

TL;DR

This paper develops new inflationary models with supersymmetry breaking using hyperbolic geometry and a gauged $U(1)_R$ symmetry, resulting in Starobinsky-like predictions consistent with CMB data.

Contribution

It introduces a novel single-superfield inflation model with supersymmetry breaking, utilizing hyperbolic Kähler geometry and a gauged $U(1)_R$ symmetry, connecting to $ ext{α}$-attractors.

Findings

Models predict $n_s$ and $r$ within $1\sigma$ CMB constraints.

Supersymmetry is broken at a high scale with a gravitino mass $\gtrsim 10^{14}$ GeV.

The inflaton is the lightest field in the model.

Abstract

We construct new models of inflation and spontaneous supersymmetry breaking in de Sitter vacuum, with a single chiral superfield, where inflaton is the superpartner of the goldstino. Our approach is based on hyperbolic K\"ahler geometry, and a gauged (non-axionic) $U(1)_R$ symmetry rotating the chiral scalar field by a phase. The $U(1)_R$ gauge field combines with the angular component of the chiral scalar to form a massive vector, and single-field inflation is driven by the radial part of the scalar. We find that in a certain parameter range they can be approximated by simplest Starobinsky-like (E-model) $\alpha$-attractors, thus predicting $n_s$ and $r$ within $1\sigma$ CMB constraints. Supersymmetry (and $R$-symmetry) is broken at a high scale with the gravitino mass $m_{3/2}\gtrsim 10^{14}$ GeV, and the fermionic sector also includes a heavy spin-$1/2$ field. In all the considered cases the inflaton is the lightest field of the model.