Density growth in Kantowski–Sachs cosmologies with a cosmological constant

Abstract

Abstract. 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 analyzed 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.PACS numbers: 04.20.-q, 98.80.Jk

Gravitational, shear and matter waves in Kantowski-Sachs cosmologies

“…In this way, a set of gauge-invariant perturbation variables can be easily identified as the ones that vanish on the chosen background [38][39][40][41][42][43][44]50]. This feature of the covariant approach makes it a very versatile method for studying perturbations on a variety of backgrounds and physical situations and relating the results obtained in a unified way [45][46][47][48][49] In this paper we present for the first time a general treatment of the vorticity-free perturbations of Kantowski-Sachs cosmologies with positive cosmological constant, extending earlier work [51], which focused only on the scalar perturbation sector. Here we present for the first time an analysis of a full scalar, vectorial and tensorial perturbations, focusing on gravitational and matter wave evolutions.…”

“…, (E.52) and (E.55) in appendix E. Substitution of these into equations (C.1)-(C.4) in appendix C of [51] reproduces the system (4.61)-(4.64).…”

“…In the spacetime given by Eq. (3.1) the non-vanishing kinematical variables of 1+1+2 formalism are the expansion [51]:…”

“…This system is equivalent to the ones describing scalar perturbations studied in [51]. Here the variables…”

Kantowski-Sachs universes sourced by a Skyrme fluid

“…In particular, Kantowski-Sachs cosmologies have been studied in a series of recent papers [32,33,35] motivated by the observed distribution of inhomogeneities and anisotropies in the cosmic background radiation, and by the possibly different evolution and propagation of perturbations in bouncing and nonbouncing cosmologies.…”