# Why is that the space-time associated with the Earth is not shrinking?

If we apply the Friedmann Lemaître equation to the Universe, we find a critical density $\rho_c$ : if the actual density $\rho$ is under it, the Universe will continue to expand, if it is higher than it, it will end in a Big-crunch.

For what reason (mathematically or physically), can't we apply Friedmann-Lemaître to the Universe's volume associated to the Earth and conclude that this portion of space-time is shrinking because the density is higher than $\rho_c$ ?

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Why it is not homogeneous ? The subvolume of the Earth, can be described as an homogeneous sphere of density $\rho$ isn't it ? –  Vincent Oct 15 '12 at 3:44