On almost Ehlers-Geren-Sachs theorems

TL;DR

This paper demonstrates that in certain Einstein-Vlasov models with Bianchi VII$_0$ symmetry, solutions can stay close to isotropic but do not necessarily become perfectly isotropic, highlighting differences from perfect fluid models.

Contribution

It generalizes previous results by showing that almost Ehlers-Geren-Sachs theorems do not hold for collisionless matter in specific symmetric cosmological models.

Findings

Solutions remain close to isotropy in shear

Shear does not tend to zero in general

Weyl curvature can blow up

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.