# Extragalactic Proper Motions: Gravitational Waves and Cosmology

## TL;DR

This paper reviews how extragalactic proper motions can be used to study cosmological phenomena, including gravitational waves and the universe's expansion, highlighting current measurements and future observational needs.

## Contribution

It provides a comprehensive overview of the effects, their signatures, and the observational strategies to detect or constrain extragalactic proper motions related to cosmology.

## Key findings

- Current measurements of proper motions are approaching the sensitivity needed to detect cosmological signals.
- Proper motions can reveal gravitational waves, large-scale structure, and Hubble expansion anisotropies.
- Predicted proper motion amplitudes are around 0.1 microarcseconds per year.

## Abstract

Extragalactic proper motions can reveal a variety of cosmological and local phenomena over a range of angular scales. These include observer-induced proper motions, such as the secular aberration drift caused by the solar acceleration about the Galactic Center and secular extragalactic parallax resulting from our motion with respect to the cosmic microwave background rest frame. Cosmological effects include the isotropy of the Hubble expansion, transverse peculiar velocities induced by large scale structure, the real-time evolution of the baryon acoustic oscillation, and long-period gravitational waves that deflect light rays, producing an apparent quadrupolar proper motion pattern on the sky. We review these effects, their imprints on global correlated extragalactic proper motions, their expected amplitudes, the current best measurements (if any), and predictions for Gaia. Finally, we describe key ground- and space-based observational requirements to measure or constrain these proper motion signals down to amplitudes of $\sim$0.1 $\mu$as yr$^{-1}$, or $\sim$0.7% of $H_0$.