On almost Ehlers-Geren-Sachs theorems

Abstract

We show assuming small data that massless solutions to the reflection symmetric Einstein-Vlasov system with Bianchi VII${}_0$ symmetry which are not locally rotational symmetric, can be arbitrarily close to and will remain close to isotropy as regards {to} the shear. However in general the shear will not tend to zero and the Hubble normalised Weyl curvature will blow up. This generalises the work \cite{NHW,WHU}, which considered a non-tilted radiation fluid to the massless Vlasov case. This represents another example of the fact that almost Ehlers-Geren-Sachs theorems do not hold in general and that collisionless matter behaves differently than a perfect fluid.

arXiv comment26 pages, 1 figure; matches accepted version in CQG; presentation improved, minor typos corrected

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• Future of Bianchi I magnetic cosmologies with kinetic matter