On the future of solutions to the massless Einstein-Vlasov system in a Bianchi I cosmology

TL;DR

This paper demonstrates that in a Bianchi I cosmology, massless Einstein-Vlasov solutions with small anisotropy asymptotically resemble a radiation fluid in Einstein-de Sitter space, with anisotropy decaying over time.

Contribution

It provides a detailed analysis of the asymptotic behavior of massless solutions in Bianchi I cosmology, showing convergence to a radiation fluid with decaying anisotropy.

Findings

Massless solutions tend to a radiation fluid in Einstein-de Sitter space.

Anisotropy decays as O(t^{-1/2}) over time.

Small initial anisotropy leads to isotropization asymptotically.

Abstract

We show that massless solutions to the Einstein-Vlasov system in a Bianchi I space-time with small anisotropy, i.e. small shear and small trace-free part of the spatial energy momentum tensor, tend to a radiation fluid in an Einstein-de Sitter space-time with the anisotropy $\Sigma^a_b\Sigma^b_a$ and $\tilde{w}^i_j \tilde{w}^j_i$ decaying as $O(t^{-\frac12})$.