Isotropization of non-diagonal Bianchi I spacetimes with collisionless matter at late times assuming small data

TL;DR

This paper proves that non-diagonal Bianchi I spacetimes with collisionless matter tend to isotropy at late times under small initial shear and velocity bounds, with Kasner exponents approaching 1/3, using a bootstrap method.

Contribution

It demonstrates late-time isotropization of such spacetimes with collisionless matter assuming small initial shear and velocity, extending understanding of anisotropic cosmological models.

Findings

Kasner exponents converge to 1/3

Asymptotic metric expression derived

Spacetimes approach dust-like behavior

Abstract

Assuming that the space-time is close to isotropic in the sense that the shear parameter is small and that the maximal velocity of the particles is bounded, we have been able to show that for non-diagonal Bianchi I-symmetric spacetimes with collisionless matter the asymptotic behaviour at late times is close to the special case of dust. We also have been able to show that all the Kasner exponents converge to 1/3 and an asymptotic expression for the induced metric has been obtained. The key was a bootstrap argument.