The deceleration parameter in perturbed Bianchi universes with a peculiar-velocity "tilt"

Bianchi cosmologies are "natural" anisotropic extensions of the Friedmann universes and they have long been used to investigate the cosmological implications of anisotropy. The latter introduces new ingredients to the standard scenarios, although there are physical processes and effects that maintain their basic Friedmann features when extended to Bianchi universes. Here, we assume a perturbed Bianchi model and look into the implications of the observers' peculiar flow for their measurement and their interpretation of the deceleration parameter. Our motivation is twofold. To begin with, relative motions have long been known to deceive the observers by "contaminating" the observations, which also still suffer from sample limitations that cloud the statistical significance of the findings. Further motivation comes from claims that observers in bulk flows that expand slightly slower than their surroundings can have the illusion of cosmic acceleration in a universe that is actually decelerating. The claim was originally based on studies of a perturbed tilted Einstein-de Sitter model, but persisted when the background cosmology was replaced by any of the three Friedmann universes. This raised the possibility that the peculiar-motion effect on the deceleration parameter may be generic and largely independent of the host spacetime. Here, we investigate this possibility by extending the earlier studies to perturbed Bianchi models. We find that the Friedmann picture remains unchanged, unless the Bianchi background has unrealistically high anisotropy. The bulk-flow observers can still be misled to the illusion of accelerated expansion by their own peculiar motion.