The Decoupling of Scalar-Modes from a Linearly Perturbed Dust-Filled Bianchi Type-I Model

We study linear perturbations about a dust filled Bianchi type-I model with the vorticity set to zero. In comparison to linear perturbations about the Friedmann–Lema?tre–Robertson–Walker models, modes of perturbations about the Bianchi type-I models are coupled. We find that the tensor that represents the background shear needs to be degenerate in order for the scalar-mode perturbations to decouple from the rest of the flow.