由SLOAN观测数据测试大尺度结构的均匀性

Test Homogeneity of Large Scale Structure from SDSS Data

宇宙学的基本假设之一是宇宙在大尺度上均匀各向同性。为了验证星系分布在大尺度上的均匀性,分别计算观测样本和观测空间几何体的分形维数,得到SDSS-DR4中星系分布的分形维数。观测空间几何体的分形维数用随机样本来确定。样本中的星系红移z的范围为0.01—0.26。当尺度持续增加至几十个Mpc时,星系分布的分形维数一致地趋向于3。所有的样本均显示了明显的转变尺度,当尺度大于此转变尺度时,星系分布的分形维数D_G～3,星系的分布转变为均匀分布。结果支持了宇宙学的基本原理关于宇宙大尺度均匀的假设。样本的转变尺度随着样本的光度增强而变大,说明小尺度上星系的分布不是简单的分形分布,而是多维分形分布。高光度星系的转变尺度非常大,直到100h^(-1) Mpc左右才变得均匀。

One of primary assumptions in cosmology is that the universe is homogeneous and isotropic at large scales. This assumption is the most important keystone of modern cosmology. In order to verify the homogeneity of galaxy distribution at large scales, we have computed the fractal dimensionality of galaxies distribution in SDSS-DR4. The fractal dimensionality of survey space geometry can be determined by random samples. The redshifts of galaxies in samples are from 0.01 to 0.26. As scale growing to dozens of Mpc, the fractal dimensionality of galaxies distribution gets close to 3. All the six samples show obvious transition scales. For scales larger than transition scale, the fractal dimensionality DG is very close to 3, which means the galaxies distribution is homogeneous. All these results support the assumption that the universe is homogeneous at large scales. The assumption is verified for scales larger than this transition scale. The transition scales increase as the luminosity of samples grows which means the distribution of galaxies is not a simple fractal distribution, but a multi-fractal distribution. This distribution becomes odd for high-luminosity galaxies. Transition scales of high-luminosity samples are very large. The samples do not become homogeneous until 100h^-1Mpc. To restrict all the cosmological parameters accurately, the effect of very large scales with odd distribution should be considered.