  Although bulk peculiar motions are commonplace in the universe, most
theoretical studies either bypass them, or take the viewpoint of the idealised
Hubble-flow observers. As a result, the role of these peculiar flows remains
largely unaccounted for, despite the fact that relative-motion effects have led
to the misinterpretation of the observations in a number of occasions. Here, we
examine the implications of large-scale peculiar flows for the interpretation
of the deceleration parameter. We compare, in particular, the deceleration
parameters measured by the Hubble-flow observers and by their bulk-flow
counterparts. In so doing, we use Newtonian theory and general relativity and
employ closely analogous theoretical tools, which allows for the direct and
transparent comparison of the two studies. We find that the Newtonian
relative-motion effects are generally too weak to make a difference between the
two measurements. In relativity, however, the deceleration parameters measured
in the two frames differ considerably, even at the linear level. This could
deceive the unsuspecting observers to a potentially serious misinterpretation
of the universe's global kinematic status. We also discuss the implications and
the observational viability of the relativistic study.
