Density growth in Kantowski-Sachs models with a cosmological constant

M. Bradley, P.K.S. Dunsby and M. Forsberg

In this work we consider the growth of density perturbations in Kantowski-Sachs models with a cosmological constant. Under certain conditions these models can undergo an anisotropic bounce where the universe changes from a contracting to an expanding phase. To study the evolution of the density perturbations we use the 1+3 and 1+1+2 covariant splits of spacetime. As inhomogeneity variables we choose the spatial gradients of the density, the expansion, the shear scalar and one more auxiliary scalar needed to close the system. The propagation equations for these quantities are then derived from the Ricci and Bianchi identities and commutator equations. The obtained system is then projected along the anisotropy and perpendicular directions respectively. By taking divergences along these directions respectively and then making the corresponding harmonic decompositions of the spatial derivatives, the system is finally reduced to a first order system in eight scalar quantities for each wave number. The growth and decay of the perturbations are then studied for different cases with special attention to the behaviour close to a bounce.