Mathematically precise formulation of Ehlers-Geren-Sachs theorem

[nick41]

I would like to get a mathematically precise formulation of the Ehlers-Geren-Sachs theorem. I have heard that this theorem roughly tells us that the universe in total is described by a FLRW metric if there exists a set of fundamental observers, with respect to whom all observable properties of the Universe are isotropic. But this in my eyes is not a mathematically precise statement and I would like to see a rigorous mathematical theorem about differential-geometric properties of spacetimes. Can you give me a reference, where I can find it?

 

[bcrowell]

See http://en.wikipedia.org/wiki/Ehlers–Geren–Sachs_theorem and footnotes in the article for references.

Also http://arxiv.org/abs/astro-ph/9501016 at "The exact isotropic case considered by Ehlers, Geren, and Sachs [32] corresponds to..."