Quantum Einstein-Dirac Bianchi Universes

TL;DR

This paper investigates the quantum behavior of Bianchi cosmological models with Dirac spinor fields, revealing unique potentials and mass terms, and provides exact solutions for Bianchi type-II, enhancing understanding of quantum cosmology with fermions.

Contribution

It introduces a finite-dimensional fermionic Hilbert space in mini-superspace quantization and solves the Bianchi type-II system exactly, highlighting novel quantum features of fermionic cosmologies.

Findings

Exact quantum solutions for Bianchi type-II system.

Identification of spin-dependent Morse-type potentials.

Discussion of quantum dynamics in classically chaotic Bianchi type-IX universe.

Abstract

We study the mini--superspace quantization of spatially homogeneous (Bianchi) cosmological universes sourced by a Dirac spinor field. The quantization of the homogeneous spinor leads to a finite-dimensional fermionic Hilbert space and thereby to a multi-component Wheeler-DeWitt equation whose main features are: (i) the presence of spin-dependent Morse-type potentials, and (ii) the appearance of a q-number squared-mass term, which is of order ${\cal O}(\hbar^2)$, and which is affected by ordering ambiguities. We give the exact quantum solution of the Bianchi type-II system (which contains both scattering states and bound states), and discuss the main qualitative features of the quantum dynamics of the (classically chaotic) Bianchi type-IX system. We compare the exact quantum dynamics of fermionic cosmological billiards to previous works that described the spinor field as being either classical or Grassmann-valued.