Tilted two-fluid Bianchi type I models

TL;DR

This paper studies the evolution of tilted two-fluid Bianchi type I cosmological models, showing conditions under which they isotropize and analyzing their asymptotic states through numerical and linear methods.

Contribution

It demonstrates that models with equal linear equations of state isotropize if and only if w ≤ 1/3, extending previous work on different fluid parameters.

Findings

Models with w=0 isotropize to the future.

Future isotropization occurs if and only if w ≤ 1/3.

Numerical and linear analyses identify asymptotic states.

Abstract

In this paper we investigate expanding Bianchi type I models with two tilted fluids with the same linear equation of state, characterized by the equation of state parameter w. Individually the fluids have non-zero energy fluxes w.r.t. the symmetry surfaces, but these cancel each other because of the Codazzi constraint. We prove that when w=0 the model isotropizes to the future. Using numerical simulations and a linear analysis we also find the asymptotic states of models with w>0. We find that future isotropization occurs if and only if $w \leq 1/3$. The results are compared to similar models investigated previously where the two fluids have different equation of state parameters.