Quantum Einstein-Dirac Bianchi Universes

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 $\mathcal{O}({\hslash }^2)$, 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.

50 pages

References in corpus (10)

• E10 and a "small tension expansion" of M Theory
• E_(10), BE_(10) and Arithmetical Chaos in Superstring Cosmology
• Hyperbolic Kac-Moody Algebras and Chaos in Kaluza-Klein Models
• Spacelike Singularities and Hidden Symmetries of Gravity
• Hidden symmetries and the fermionic sector of eleven-dimensional supergravity
• Extended E8 Invariance of 11-Dimensional Supergravity
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• K(E10), Supergravity and Fermions
• Hidden Symmetries and Dirac Fermions
• Fermionic Kac-Moody Billiards and Supergravity

Cited by in corpus (12)

• Quantum Supersymmetric Bianchi IX Cosmology
• On the cosmological singularity
• Quantum Supersymmetric Cosmology and its Hidden Kac-Moody Structure
• Cosmological evolution of equation of state for dark energy in G-essence models
• On the dynamics of the general Bianchi IX spacetime near the singularity
• Spinor driven cosmic bounces and their cosmological perturbations
• On higher spin realizations of K(E10)
• Some examples of different descriptions of energy-momentum density in the context of Bianchi IX cosmological model
• Non-minimally coupled nonlinear spinor field in FRW cosmology
• Reconstruction of the equation of state for the cyclic universes in homogeneous and isotropic cosmology
• Matter-antimatter asymmetry in a rotating universe: Dirac spinors in axisymmetric Bianchi IX cosmology
• On FLRW reductions of N=1 supergravity