COVARIANT PERTURBATIONS OF ANISOTROPIC COSMOLOGICAL MODELS

In this paper I use the covariant approach to study the evolution of l inear perturbations in a Bianchi type-I cosmology. It is found that th e evolution of density perturbations is described by a fourth-order sy stem of differential equations as in the treatment of Perko, Matzner, and Shepley for the case of a pressureless perfect fluid and I verify that these equations are consistent using the set of linear constraint equations. I then show that when the shear is axially symmetric this system reduces to one second-order differential equation for the densi ty gradient. Approximate solutions are found for the case of dust, whi ch are in agreement with earlier studies. I also consider a recently d eveloped dynamic systems approach to discuss the qualitative behavior of the solutions and the stability of Bianchi type-I models with respe ct to linear inhomogeneous perturbations.