The peculiar Jeans length

Large-scale bulk flows are commonplace in the universe. This means that observers living in typical galaxies, like our Milky Way, do not follow the mean universal expansion, but have peculiar velocities relative to it. Using relativistic linear cosmological perturbation theory, we show that bulk peculiar motions introduce a characteristic length scale. The latter is analogous to the familiar Jeans length and marks the threshold below which the linear kinematics, as seen by observers living inside the bulk flow, are dominated by relative-motion effects. On these scales cosmological measurements can vary considerably between the rest-frame of the bulk flow and that of the smooth Hubble expansion, due to relative-motion effects alone. In this work, we look into and compare the measurements of the deceleration parameter. We find that the associated "peculiar Jeans length" has typical size of the order of few hundred Mpc. On smaller scales, the deceleration parameter measured by the bulk-flow observers can be considerably larger (or lower) than its Hubble-frame counterpart. This, in turn, depends on whether the peculiar motion is slightly expanding (or contracting) relative to the background universal expansion. Then, assuming that expanding and contracting bulk flows are randomly distributed, nearly half of the observers in the universe may be misled to think that their cosmos is over-decelerated. The rest of them, on the other hand, may come to believe that the universe is under-decelerated, or even accelerated in some cases.