具有动力学曲率的宇宙模型
Cosmological model with dynamical curvature
摘要：
最近引入的相对论拉格朗日暗子流体模型（EPJ C（2015）75：9）被推广到自引力、无旋、无压力和无应力的测地流体，其能量-动量张量是具有非平凡能量流的尘埃，定义了我们宇宙学模型的一般框架。在本文中，我们只考虑在非常大的尺度上宇宙的平均动力学，使我们能够与共形平坦几何。相应的协变传播和约束方程处理在一个剪切自由的非相对论性限制。动力学描述与拉格朗日在minisuperspace。利用两个条件动力学对称性，得到了能量密度、哈勃函数和空间曲率的一阶相对论修正的解析解。这导致了一个宇宙学模型，其中宇宙的加速膨胀是由时间依赖的空间曲率驱动的，而不需要引入任何类型的暗能量。此外，还导出了面积距离的微分方程。
英文摘要：
The recently introduced relativistic Lagrangian darkon fluid model (EPJ C (2015) 75:9) is generalized to a self-gravitating, irrotational, pressure-less and stress free geodesic fluid, whose energy-momentum tensor is dust-like with nontrivial energy flow, defining the general framework for our cosmological model. In the present paper we consider only the averaged dynamics of the Universe at very large scales, allowing us to work with conformal flat geometry. The corresponding covariant propagation and constraint equations are treated in a shear-free nonrelativistic limit. The dynamics is described with a Lagrangian in minisuperspace. Analytic solutions for the energy density, the Hubble function and the 1st order relativistic correction to the spatial curvature are obtained by means of two conditional dynamical symmetries. This leads to a cosmological model where the accelerated expansion of the Universe is driven by a time-dependent spatial curvature without the need for introducing any kind of dark energy. A differential equation for the area distance is derived in addition.
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