The peculiar Jeans length

TL;DR

This paper introduces the concept of a 'peculiar Jeans length' related to observers' bulk motions, showing it can significantly affect local measurements of cosmic deceleration and potentially lead to misinterpretations of the universe's expansion.

Contribution

It proposes the 'peculiar Jeans length' as a new scale affecting cosmological measurements, highlighting how relative motions can bias interpretations of cosmic acceleration.

Findings

Peculiar motions introduce a characteristic scale affecting linear kinematics.

The peculiar Jeans length varies between a few and several hundred Mpc.

Observers' relative motions can cause misinterpretations of the universe's deceleration.

Abstract

Typical observers in the universe do not follow the smooth Hubble expansion, but move relative to it. Such bulk peculiar motions introduce a characteristic scale that is closely analogous to the familiar Jeans length. This "peculiar Jeans length" marks the threshold below which relative-motion effects dominate the linear kinematics. There, cosmological measurements can vary considerably between the bulk-flow frame and that of the Hubble expansion, entirely due to the observers' relative motion. When dealing with the deceleration parameter, we find that the peculiar Jeans length varies between few and several hundred Mpc. On these scales, the deceleration parameter measured by the bulk-flow observers can be considerably larger (or smaller) than its Hubble-frame counterpart. This depends on whether the peculiar motion is locally expanding (or contracting), relative to the background expansion. Then, provided expanding and contracting bulk flows are randomly distributed, nearly half of the observers in the universe could be misled to think that their cosmos is over-decelerated. The rest of them, on the other hand, may come to believe that their universe is under-decelerated, or even accelerated in some cases. We make two phenomenological predictions that could in principle support this scenario.