Density growth in Kantowski-Sachs cosmologies with a cosmological constant

In this work, the growth of density perturbations in Kantowski-Sachs cosmologies with a positive cosmological constant is studied, using the 1+3 and 1+1+2 covariant formalisms. For each wave number, we obtain a closed system for scalars formed from quantities that are zero on the background and hence are gauge-invariant. The solutions to this system are then analysed both analytically and numerically. In particular, the effects of anisotropy and the behaviour close to a bounce in the cosmic scale factor are considered. We find that typically the density gradient in the bouncing direction experiences a local maximum at or slightly after the bounce. (paper)