Cosmological perturbations in Bianchi type-I universes

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Abstract
The evolution equations for small perturbations in the metric, energy density, and material velocity are derived for an anisotropic viscous Bianchi type-I universe. The equations obtained are the same as those found by Perko, Matzner, and Shepley, and by Tomita and Den. However, the splitting up of these equations is different from the way it is performed by these authors, which results in the fact that, in close analogy with the flat Friedmann-Robertson-Walker universe, the general solution of the perturbation equations can be split up into three noncoupled perturbations: namely, gravitational waves (‘‘tensor perturbations’’), vortex motions (‘‘vector perturbations’’), and density enhancements (‘‘scalar perturbations’’). Moreover, the results are independent of the equation of state of the cosmic fluid and its viscosity. The gravitational waves need not necessarily be transversal in an anisotropically expanding Bianchi type-I universe. It is shown, however, that the longitudinal components of the gravitational waves have no physical significance.

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