Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-03-15
Phys.Rev.D83:123520,2011
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
50 pages
Scientific paper
10.1103/PhysRevD.83.123520
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.
Damour Thibault
Spindel Philippe
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