空间均匀各向同性的Einstein-Dirac宇宙学
A Spatially Homogeneous and Isotropic Einstein-Dirac Cosmology
摘要：
考虑一个空间均匀各向同性的宇宙模型，其中Dirac旋量与经典引力耦合。对于狄拉克旋量，我们选择一个Hartree-Fock模型，其中所有的单粒子波函数都是相干的，并且具有相同的动量。如果尺度函数很大，宇宙的行为就像经典的弗里德曼尘埃溶液。然而，如果标度函数很小，量子效应会导致能量-动量张量的振荡。数值计算和解析证明了这些量子振荡可以阻止大爆炸或大挤压奇点的形成。分析了能源条件。我们证明了时间周期解的存在性，它经历了无限多个膨胀和收缩周期。
英文摘要：
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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