简单Kaluza-Klein宇宙学的再考察
Re-Examination of Simple Kaluza-Klein Cosmologies
摘要：
简单的宇宙学模型的基础上五维卡鲁扎-克莱因相对论的重新审查和有趣的性质表示。这些模型是Davidson等人以及Mann和Vincent得到的模型的特例，特别是那些宇宙学常数为零的模型。不存在五维源：解在五维中是里奇平坦的。假设电磁自由度不被激发，因此由降维引起的四维应力-能量张量完全是由于标量场，服从辐射状态方程。对于曲率指数的三种选择，标度因子对宇宙时间的依赖性对应于：当k = -1时，反弹或大爆炸;当k = 0时，大爆炸;当k = 1时，大爆炸后坍缩。Kretschmann标量与加速度的平方成比例，并且在k = -1和k = 0时接近于零，同时在某些情况下揭示真正的奇点。其中只有一个模型表现出了现实的K-K模型所希望的紧化行为：在最早的时候，第五维的周长收缩，然后是一段较长的稳定期。
英文摘要：
Simple cosmological models based upon five-dimensional Kaluza-Klein relativity are re-examined and interesting properties are indicated. These models are special cases of those obtained by Davidson et al. and Mann and Vincent, specifically, those with vanishing cosmological constant. No five-dimensional sources are present: the solutions are Ricci-flat in five dimensions. Electromagnetic degrees of freedom are assumed not to be excited, consequently the four-dimensional stress-energy tensor induced by dimensional reduction is entirely due to the scalar field, obeying the radiation equation of state. For the three choices of curvature index, the dependence of the scale factor on cosmic time corresponds to, for k = -1 either a bounce or big bang, for k = 0 a big bang, and for k = 1 a big bang followed by collapse. The Kretschmann scalar is proportional to the square of acceleration and approaches zero for k = -1 and k = 0, while revealing true singularities in some cases. Only one of the models exhibits the compactification behavior hoped for in a realistic K-K model: shrinking of the circumference of fifth dimension in the earliest times followed by an extended period of stability.
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