Perturbations of an anisotropic spacetime: Dust filled medium

We investigate the evolution of a perturbed Bianchi type-I universe filled with a (pressureless) dust medium. The background model shows a smooth transition from the early shear-dominated anisotropic stage to the dust-dominated isotropic stage. We have exact solutions describing the background evolution. We consider the situations where the perturbation wave vector lies in a plane made of two principal axes of the background anisotropy. We take the comoving gauge. We numerically investigate the behavior of perturbation as it goes through the transition. The results show that in the shear-dominated stage the density perturbation shows the coupling with the gravitational wave perturbations. Because of the coupling the density perturbation in the small scale shows an oscillatory behavior with a decreasing amplitude.