Bianchi type I models with two tilted fluids

TL;DR

This paper studies Bianchi type I cosmological models with two tilted fluids, revealing conditions under which the universe isotropizes or remains anisotropic based on fluid properties and asymptotic behavior.

Contribution

It introduces a detailed analysis of Bianchi type I models with two tilted fluids, highlighting how fluid stiffness and sound speed influence isotropization and anisotropic outcomes.

Findings

Models approach Kasner states near the past singularity.

Isotropization occurs if one fluid has sound speed ≤ 1/3 of light.

Final anisotropic state if both fluids are stiffer than radiation.

Abstract

In this paper we investigate expanding Bianchi type I models with two tilted fluids with linear equations of state. Individually the fluids have non-zero energy fluxes w.r.t. the symmetry surfaces, but these cancel each other because of the Codazzi constraint. Asymptotically toward the past the solutions approach Kasner states if the speeds of sound are less than that of light. If one of the fluids has a speed of sound that is less or equal to 1/3 of the speed of light (radiation) then the models isotropize toward the future, but if both fluids are stiffer than radiation then the final state is anisotropic with non-zero Hubble-normalized shear. The significance of these results is discussed in a broader context.