In a systematic study, we use an equivalent pair of improved numerical relativity codes based on a tetrad-formulation of the classical Einstein-scalar field equations to examine whether slow contraction or inflation (or both) can resolve the homogeneity, isotropy and flatness problems. Our finding, based on a set of gauge/frame invariant diagnostics and the models considered, is that slow contraction robustly and rapidly smooths and flattens spacetime beginning from initial conditions that are outside the perturbative regime of the flat Friedmann-Robertson-Walker metric, whereas inflation fails these tests. We present new numerical evidence supporting the conjecture that the combination of ultralocal evolution and an effective equation-of-state with pressure much greater than energy density is the key to having robust and rapid smoothing. The opposite of ultralocality occurs in expanding spacetimes, which is the leading obstruction to smoothing following a big bang.

中文翻译：

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通过缓慢收缩与膨胀来平滑宇宙


在一项系统研究中，我们使用一对基于经典爱因斯坦标量场方程四分体公式的等效改进数值相对论代码来检验缓慢收缩或膨胀（或两者）是否可以解决均匀性、各向同性和平坦度问题。基于一组规范/框架不变诊断和所考虑的模型，我们的发现是，慢收缩从平面弗里德曼-罗伯逊-沃克度量的微扰范围之外的初始条件开始，稳健且快速地平滑和展平时空，而通货膨胀未能通过这些测试。我们提出了新的数值证据，支持这样的猜想：超局部演化和压力远大于能量密度的有效状态方程的结合是实现鲁棒和快速平滑的关键。超定域性的反面发生在时空扩张中，这是大爆炸后平滑的主要障碍。