N=2 Supersymmetry and de Sitter space

TL;DR

This paper explores a unique de Sitter solution within N=2 supersymmetry, demonstrating a model with hybrid inflation potential that spontaneously breaks all supersymmetries during inflation and restores some afterward, potentially explaining cosmic acceleration.

Contribution

It introduces a novel N=2 supersymmetric model with a hybrid inflation potential capable of producing de Sitter space and describes supersymmetry breaking and restoration mechanisms.

Findings

De Sitter stage exists when SU(2,2|2) symmetry is softly broken to N=2 supersymmetry.

The model exhibits a hybrid inflation potential with a slow-roll regime.

Post-bifurcation, the system transitions to a ground state with partial supersymmetry restoration.

Abstract

We present a (unique?) possibility of de Sitter solution in the framework of N=2 supersymmetry (hypersymmetry). We show that a model with a vector and a charged hypermultiplet has a hybrid inflation type potential. It leads to a slow-roll regime in de Sitter type background with all supersymmetries broken spontaneously. Beyond the bifurcation point the waterfall stage abruptly brings the system into a ground state with 2 unbroken supersymmetries. De Sitter stage exists under condition that the superconformal SU(2,2|2) symmetry of the model is softly broken down to N=2 supersymmetry by the vev of the Killing prepotential triplet P^r. This hybrid hypersymmetry model may describe P-term inflation and/or acceleration of the universe at the present epoch.