A Spatially Homogeneous and Isotropic Einstein-Dirac Cosmology

TL;DR

This paper explores a cosmological model with Dirac spinors coupled to gravity, showing quantum effects can prevent singularities and lead to cyclic universe solutions.

Contribution

It introduces a Hartree-Fock ansatz for Dirac spinors in cosmology and demonstrates quantum oscillations can avoid big bang or crunch singularities.

Findings

Quantum oscillations prevent singularities.

Existence of cyclic, time-periodic solutions.

Behavior matches classical solutions at large scales.

Abstract

We consider a spatially homogeneous and isotropic cosmological model where Dirac spinors are coupled to classical gravity. For the Dirac spinors we choose a Hartree-Fock ansatz where all one-particle wave functions are coherent and have the same momentum. If the scale function is large, the universe behaves like the classical Friedmann dust solution. If however the scale function is small, quantum effects lead to oscillations of the energy-momentum tensor. It is shown numerically and proven analytically that these quantum oscillations can prevent the formation of a big bang or big crunch singularity. The energy conditions are analyzed. We prove the existence of time-periodic solutions which go through an infinite number of expansion and contraction cycles.