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Naturally we have to consider universes outside the family of Robertson-Walker spaces, ie globally non-isotropic/non-homogeneous geometries.
As mentioned in the previous lecture, the above theory can be carried over fairly easily to non-isotropic settings, such as that given by the, which is holomorphically equivalent to the Siegel upper half-space
The second term becomes for a non-isotropic polarizibility in three different, but fully equivalent, notations,
On the other hand, Einstein encouraged LemaÃ®tre to look into the possibility of non-isotropic expansion models, so it’s clear he was not dismissive of the concept altogether.
"Gives us more volume, better turbulence, but there's also a non-isotropic pressure drop, which cuts into our efficiency ....
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