Bulk flows in the local Universe and the importance of relativistic effects

TL;DR

This paper examines relativistic effects on bulk flow velocity estimates in the local universe, providing a formula that improves accuracy and reveals a bias in recent measurements.

Contribution

It introduces a cosmographic formula incorporating relativistic effects for precise bulk flow estimation, highlighting a significant bias in previous measurements.

Findings

Relativistic effects cause a ~10% bias in bulk flow estimates.

The new formula improves the accuracy of bulk flow measurements.

Relativistic corrections become more important at larger scales.

Abstract

Bulk flow velocities are typically estimated in the idealised picture where observers are moving within a perfectly homogeneous and isotropic space-time. This picture is consistent within standard perturbation theory up to relativistic effects that lead to correction terms of order $v z$, where $z$ is the redshift of observation, and $v$ is the amplitude of the bulk flow. The dominant relativistic contributions at scales $z \lesssim 1$ are caused by gravitational redshift and time evolution of the velocity field. We include these effects within a broadly applicable weak-field approximation, and provide a cosmographic formula for estimating bulk flows at a high precision. Based on this formula, we judge that recent bulk flow estimates are biased toward larger values by $\sim 10\%$. This theoretical bias surpasses the measurement biases of the same estimates, and it will become still more important to account for the relativistic effects as the scales at which bulk flows are estimated to increase.