Testing the Cosmological Principle: Astrometric Limits on Systemic Motion of Quasars at Different Cosmological Epochs

TL;DR

This study uses Gaia EDR3 data to analyze quasar proper motions across different redshifts, finding no significant systemic motion variations, thus testing the cosmological principle at large scales.

Contribution

It introduces a novel method of fitting proper motion fields with Zernike functions across redshift bins to test for systemic motions in quasars.

Findings

Detected a large-scale gradient in proper motions at redshift ~1.52

No significant small- or medium-scale systemic variations with redshift

Instrumental effects likely cause some observed patterns

Abstract

A sample of $60,410$ bona fide optical quasars with astrometric proper motions in Gaia EDR3 and spectroscopic redshifts above 0.5 in an oval 8400 square degree area of the sky is constructed. Using orthogonal Zernike functions of polar coordinates, the proper motion fields are fitted in a weighted least-squares adjustment of the entire sample and of six equal bins of sorted redshifts. The overall fit with 37 Zernike functions reveals a statistically significant pattern, which is likely to be of instrumental origin. The main feature of this pattern is a chain of peaks and dips mostly in the R.A. component with an amplitude of 25~$\mu$as yr$^{-1}$. This field is subtracted from each of the six analogous fits for quasars grouped by redshifts covering the range 0.5 through 7.03, with median values 0.72, 1.00, 1.25, 1.52, 1.83, 2.34. The resulting residual patterns are noisier, with formal uncertainties up to 8~$\mu$as yr$^{-1}$ in the central part of the area. We detect a single high-confidence Zernike term for R.A. proper motion components of quasars with redshifts around 1.52 representing a general gradient of 30 $\mu$as yr$^{-1}$ over $150\degr$ on the sky. We do not find any small- or medium-scale systemic variations of the residual proper motion field as functions of redshift above the $2.5\,\sigma$ significance level.