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.
