A 0.002% perturbation to the flat FRLW metric is sufficient to model the observed universe granularity

We introduce a small perturbation term into the flat pressure-free FRLW cartesian metric. The derivation of the Einstein fields equations shows that this modified metric describes an inhomogeneous universe. Interestingly, the derived expanding rate equation is that of the flat isotropic pressure-free homogeneous FLRW model. A perturbation term modelling any galaxy distribution is provided and analysed. A maximal relative deviation of the modified metric from the original one smaller than 0.002% is sufficient to model galaxy bulge and inter-galaxy medium densities. This results from the fact that the Hubble constant is about 5 orders of magnitude smaller than the speed of light divided by typical galaxy diameter. This approached metric has the benefit to allow a direct physical interpretation of the coordinates. It also supports the validity of the Ia type supernovae distances assessments.我们在平坦无压强的FRLW（Friedmann-Lemaître-Robertson-Walker）笛卡尔度规中引入了一个微小扰动项。通过爱因斯坦场方程（Einstein field equations）的推导可知，该修正后的度规可描述非均匀宇宙。值得注意的是，推导得到的膨胀速率方程与平坦各向同性无压强均匀FLRW模型的膨胀速率方程完全一致。本文还给出并分析了一个可用于模拟任意星系分布的扰动项。修正后度规与原始度规的最大相对偏差仅需小于0.002%，即可模拟星系核球与星系际介质的密度分布。这一结论源于哈勃常数（Hubble constant）较“光速除以典型星系直径”的结果小约5个数量级。该近似度规的优势在于可对坐标系进行直接物理解释，同时也可验证Ia型超新星（Type Ia Supernovae）距离测定的合理性。