在捨棄宇宙學原理中的均勻性下，考慮一個全由物質組成，球對稱、在徑向上物質分佈不均勻的簡單宇宙模型，LTB模型。測試一已知宇宙加速膨脹的數學例子，並將理論推導延伸至實際物理觀測量－紅移。僅僅是物質在空間分布具變化的概念也可以得出不引用任何暗能量也可以看得到如同在超新星觀測資料中發現的宇宙加速膨脹現象。

Giving up the homogeneity of the cosmological principle that holds for decades , I consider a spherically symmetric but inhomogeneous Lemaitre -Tolman-Bondi (LTB) metric , which provides an simple toy model for an inhomogeneous universe. To examine an already known mathematical example, I derive the appropriate equations which determine the definition of the redshift. Without dark energy , the accelerating expansion observed by distant supernova data can also be described by spatial variation in matter density.

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