# Relativistic approach to the kinematics of large-scale peculiar motions

## TL;DR

This paper uses relativistic cosmological perturbation theory to analyze large-scale peculiar motions, revealing faster growth rates than previous Newtonian models, especially near and beyond the Hubble radius.

## Contribution

It provides a relativistic analysis of peculiar velocity growth, showing that bulk flows grow faster than Newtonian predictions due to relativistic effects.

## Key findings

- Peculiar velocities grow as a^2 near and beyond the Hubble radius.
- Relativistic effects enhance the growth rate of bulk flows.
- Faster peculiar velocities imply larger, more rapid bulk flows than previously expected.

## Abstract

We consider the linear kinematics of large-scale peculiar motions in a perturbed Friedmann universe. In so doing, we take the viewpoint of the "real" observers that move along with the peculiar flow, relative to the smooth Hubble expansion. Using relativistic cosmological perturbation theory, we study the linear evolution of the peculiar velocity field, as well as the expansion/contraction, the shear and the rotation of the bulk motion. Our solutions show growth rates considerably stronger than those of the earlier treatments, which were mostly Newtonian. On scales near and beyond the Hubble radius, namely at the long-wavelength limit, peculiar velocities are found to grow as $a^2$, in terms of the scale factor, instead of the Newtonian $a^{1/2}$-law. We attribute this to the fact that, in general relativity, the energy flux, triggered here by the peculiar motion of the matter, also contributes to the local gravitational field. In a sense, the bulk flow gravitates, an effect that has been bypassed in related relativistic studies. These stronger growth-rates imply faster peculiar velocities at horizon crossing and higher residual values for the peculiar-velocity field. Alternatively, one could say that our study favours bulk peculiar flows larger and faster than anticipated.