The deceleration parameter in `tilted' Friedmann universes

Large-scale peculiar motions are believed to reflect the local inhomogeneity and anisotropy of the universe, triggered by the ongoing process of structure formation. As a result, realistic observers do not follow the smooth Hubble flow but have a peculiar, `tilt', velocity relative to it. Our Local Group of galaxies, in particular, moves with respect to the universal expansion at a speed of roughly 600~km/sec. Relative motion effects are known to interfere with the observations and their interpretation. The strong dipolar anisotropy seen in the Cosmic Microwave Background, for example, is not treated as a sign of real universal anisotropy, but as a mere artifact of our peculiar motion relative to the Hubble flow. With these in mind, we look into the implications of large-scale bulk motions for the kinematics of their associated observers, by adopting a `tilted' Friedmann model. Our aim is to examine whether the deceleration parameter measured in the rest-frame of the bulk flow can differ from that of the actual universe due to relative-motion effects alone. We find that there is a difference, which depends on the speed as well as the scale of the bulk motion. The faster and the smaller the drifting domain, the larger the difference. In principle, this allows relatively slow peculiar velocities to have a disproportionately strong effect on the value of the deceleration parameter measured by observers within bulk flows of, say, few hundred megaparsecs. In fact, under certain circumstances, it is even possible to change the sign of the deceleration parameter. It goes without saying that all these effects vanish identically in the Hubble frame, which makes then an illusion and mere artifact of the observers' relative motion.