Canonical D = 1 supergravity framework for FLRW cosmology

TL;DR

This paper develops a supersymmetric extension of flat FLRW cosmology with matter, leading to a Dirac-like quantum equation whose solutions reveal quantized or continuous universe growth rates depending on the model.

Contribution

It introduces a D=1, N=1 supergravity framework for FLRW cosmology and derives a novel Dirac-like quantum equation for the universe's evolution.

Findings

Quantized volume growth in the compact model due to zero-point energy.

Continuous spectrum of growth rates in the non-compact model with an uncertainty relation.

Solutions based on supersymmetric sigma-models for specific matter configurations.

Abstract

We construct an extension of standard flat FLRW cosmology with matter, possessing local D = 1, N = 1 proper-time supersymmetry. The fundamental equation for the resulting mini-superspace models of quantum universes is a Dirac-like analogue of the Friedmann and Wheeler-DeWitt equations. We provide solutions of this equation for specific matter configurations based on the supersymmetric O(3) and O(2, 1) sigma-models. It turns out that in the compact model the volume rate of growth of the universe is quantized and non-vanishing due to the zero-point energy of the scalar fields. In the non-compact model the spectrum of the growth rates is continuous but subject to an uncertainty relation involving the scale and the growth factor.