Finster, Felix and Hainzl, Christian
A spatially homogeneous and isotropic Einstein–Dirac cosmology.
Journal of Mathematical Physics 52, 042501.
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.
|Date:||6 April 2011|
|Institutions:|| Mathematics > Prof. Dr. Felix Finster|
|Keywords:||cosmology, Einstein field equations, gravitation, oscillations, tensors, wave functions |
|Subjects:||500 Science > 510 Mathematics|
|Refereed:||Yes, this version has been refereed|
|Created at the University of Regensburg:||Yes|
|Deposited On:||12 Nov 2012 14:09|
|Last Modified:||12 Nov 2012 14:09|