论文标题
宇宙中的比例对称性
Scale Symmetry in the Universe
论文作者
论文摘要
比例对称性是物理学的基本对称性，但是在宇宙中似乎并未完全实现。在这里，我们专注于由重力统治的天文量表，在该量表中，比例对称性保持并引起物质的真正不变分布，即产生分形的几何形状。非线性Poisson-boltzmann- emden方程提供了对分形宇宙质量分布特征的合适解释。该方程式的替代解释与量子重力理论有关。我们研究方程的分形溶液，并将它们与随机乘法级联反应的统计理论联系起来，该理论起源于流体湍流理论。如此获得的多型质量分布的类型与宇宙学模拟分析和观察星系分布的结果一致。
Scale symmetry is a fundamental symmetry of physics that seems however not to be fully realized in the universe. Here, we focus on the astronomical scales ruled by gravity, where scale symmetry holds and gives rise to a truly scale invariant distribution of matter, namely it gives rise to a fractal geometry. A suitable explanation of the features of the fractal cosmic mass distribution is provided by the nonlinear Poisson--Boltzmann--Emden equation. An alternative interpretation of this equation is connected with theories of quantum gravity. We study the fractal solutions of the equation and connect them with the statistical theory of random multiplicative cascades, which originated in the theory of fluid turbulence. The type of multifractal mass distributions so obtained agrees with results from the analysis of cosmological simulations and of observations of the galaxy distribution.
