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An approximation scheme is developed in order to construct the metric representing a realistic fully inhomogeneous universe. The spatial averaging is used to express the fact that the expansion of the universe is generated collectively by the inhomogeneous matter distribution. The scheme allows one to calculate the back reaction due to the growth of local inhomogeneities on the expansion and vice versa. Also the expression of the deviation from Friedman–Lemaitre (FL) expansion is derived in terms of inhomogeneities. The post-Newtonian approximation is conveniently applied to solve the scheme perturbatively.
Toshifumi Futamase (Wed,) studied this question.