Supersymmetric FRW model and the ground state of supergravity

TL;DR

This paper constructs a supersymmetric FRW cosmological model within supergravity, analyzing vacuum configurations, scalar potentials, and spontaneous supersymmetry breaking, and explores the quantum states of the universe in this framework.

Contribution

It introduces a new supersymmetric FRW model with scalar matter fields, detailing the vacuum structure, potential dependence on the Kähler potential, and quantum states in supergravity.

Findings

Scalar potential depends on Kähler potential and parameter α

Vacuum states are classified by parameter α

Quantum states include zero-energy wave functions of the universe

Abstract

In this work we construct the vacuum configuration of supergravity interacting with homogeneous complex scalar matter fields. The corresponding configuration is of the FRW model invariant under the $n=2$ local conformal time supersymmetry, which is a subgroup of the four dimensional space-time supersymmetry. We show, that the potential of the scalar matter fields is a function of the K\"ahler potential and of the arbitrary parameter $\alpha$. This parameter enumerates the vacuum states. The scalar matter potential induces the spontaneous breaking of supersymmetry in supergravity. On the quantum level our model is a specific supersymmetric quantum mechanics, which admits quantum states in supergravity, and the states with zero energy are described by the wave function of the FRW universe.