Abstract
We consider a spatially homogeneous and isotropic system of Dirac particles coupled to classical gravity. The dust and radiation dominated closed Friedmann-Robertson-Walker space-times are recovered as limiting cases. We find a mechanism where quantum oscillations of the Dirac wave functions can prevent the formation of the big bang or big crunch singularity. Thus before the big crunch, the collapse of the universe is stopped by quantum effects and reversed to an expansion, so that the universe opens up entering a new era of classical behavior.
Numerical examples of such space-times are given, and the dependence on various parameters is discussed. Generically, one has a collapse after a finite number of cycles. By fine-tuning the parameters we construct an example of a space-time which satisfies the dominant energy condition and is time-periodic, thus running through an infinite number of contraction and expansion cycles.
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References
Bojowald, M.: How quantum is the big bang? Phys. Rev. Lett. 100, 221301 (2008). arXiv:0805.1192 [gr-qc]
Demianski, M., de Ritis, R., Platania, G., Scudarello, P., Stornaiolo, C.: Inflation in a Bianchi I-type Einstein-Cartan cosmological model. Phys. Rev. D 35(4), 1181–1184 (1987)
Finster, F.: Local U(2,2) symmetry in relativistic quantum mechanics. J. Math. Phys. 39(12), 6276–6290 (1998). arXiv:hep-th/9703083
Finster, F., Hainzl, C.: A spatially homogeneous and isotropic Einstein-Dirac cosmology (2009, in preparation)
Finster, F., Smoller, J., Yau, S.-T.: Particlelike solutions of the Einstein-Dirac equations. Phys. Rev. D 59(10), 104020 (1999). 19 pp., arXiv:gr-qc/9801079
Padmanabhan, T., Narlikar, J.V.: Quantum conformal fluctuations in a singular space-time. Nature 259, 677–678 (1982)
Parker, L., Fulling, S.A.: Quantized matter fields and the avoidance of singularities in general relativity. Phys. Rev. D 7(6), 2357–2374 (1974)
Penrose, R., Rindler, W.: Spinors and Space-Time, vol. 1. Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge (1987)
Toporensky, A.V.: Chaos in closed isotropic cosmological models with steep scalar field potential. Int. J. Mod. Phys. D 8, 677–678 (1999)
Turok, N., Perry, M., Steinhardt, P.J.: M theory model of a big crunch/big bang transition. Phys. Rev. D 70(10), 106004 (2004). 18 pp., arXiv:hep-th/0408083
Wetterich, C.: Quintessence—the dark energy in the universe? Space Sci. Rev. 100, 195–206 (2002). arXiv:astro-ph/0110211
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F. Finster was partially supported by the Deutsche Forschungsgemeinschaft.
C. Hainzl was partially supported by US National Science Foundation, grant DMS-0800906.
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Finster, F., Hainzl, C. Quantum Oscillations Can Prevent the Big Bang Singularity in an Einstein-Dirac Cosmology. Found Phys 40, 116 (2010). https://doi.org/10.1007/s10701-009-9380-z
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DOI: https://doi.org/10.1007/s10701-009-9380-z