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.
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April 2011
Research Article|
April 06 2011
A spatially homogeneous and isotropic Einstein–Dirac cosmology
Felix Finster;
Felix Finster
a)
1Fakultät für Mathematik,
Universität Regensburg
, D-93040 Regensburg, Germany
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Christian Hainzl
Christian Hainzl
b)
2Mathematisches Institut,
Universität Tübingen
, D-72076 Tübingen, Germany
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a)
Electronic mail: Felix.Finster@mathematik.uni-regensburg.de.
b)
Electronic mail: christian.hainzl@uni-tuebingen.de.
J. Math. Phys. 52, 042501 (2011)
Article history
Received:
February 01 2011
Accepted:
February 17 2011
Citation
Felix Finster, Christian Hainzl; A spatially homogeneous and isotropic Einstein–Dirac cosmology. J. Math. Phys. 1 April 2011; 52 (4): 042501. https://doi.org/10.1063/1.3567157
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